Analytical Geometry 2

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    Analytical Geometry 2Problem 1: CE Board May 1995What is the radius of the circle x2 + y2 – 6y = 0?

    • A. 2

    B. 3• C. 4

    • D.Problem 2: CE Board November 1995What are the coordi!ates of the ce!ter of the cur"e x2 + y2 – 2x – 4y – 3# = 0?

    • A. $%#& %#'

    • B. $%2& %2'

    • C. $#& 2'

    • D. $2& #'Problem 3:A circle (hose e)uatio! is x2 + y2 + 4x +6y – 23 = 0 has its ce!ter at

    • A. $2& 3'

    • B. $3& 2'

    • C. $%3& 2'

    • D. $%2& %3'Problem 4: ME Board April 199What is the radius of a circle (ith the *. e)uatio! x2 – 6x + y2 – 4y – #2 = 0

    • A. 3.46

    • B. ,

    • C.

    • D.6Problem 5: ECE Board April 199 -he diaeter of a circle descri/ed /y x2 + y2 = #6 is?

    • A. 413

    B. #61• C. 13

    • D.4Problem !: CE Board May 199!o( far fro the y%axis is the ce!ter of the cur"e 2x2 + 2y2 +#0x – 6y – =0

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    • A. %2.

    • B. %3.0

    • C. %2.,

    • D.%3.2Problem ":What is the dista!ce /et(ee! the ce!ters of the circles x2 + y2 + 2x + 4y – 3= 0 a!d x2 + y2 + 2x – x – 6y + , = 0?

    • A. ,.0,

    • B. ,.,,

    • C. .0,

    • D.,.,Problem : CE Board November 1993

     -he shortest dista!ce fro A $3& ' to the circle x2

    + y2

    + 4x – 6y = #2 is e)ualto?

    • A. 2.#

    • B. 2.3

    • C. 2.

    • D.2.,Problem 9: ME Board #ctober 199! -he e)uatio! circle x2 + y2 – 4x + 2y – 20 = 0 descri/es

    A. A circle of radius ce!tered at the orii!.• B. A! ecli5se ce!tered at $2& %#'.

    • C. A s5here ce!tered at the orii!.

    • D.A circle of radius ce!tered at $2& %#'.Problem 1$: EE Board April 199"

     -he ce!ter of a circle is at $#& #' a!d o!e 5oi!t o! its circufere!ce is $%#& %3'.i!d the other e!d of the diaeter throuh $%#& %3'.

    • A. $2& 4'

    • B. $3& '

    • C. $3& 6'

    • D. $#& 3'Problem 11:i!d the area $i! s)uare u!its' of the circle (hose e)uatio! is x 2 + y2 = 6x –y.

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    • A. 20 7

    • B. 22 7

    • C. 2 7

    • D. 2, 7Problem 12:

    Deteri!e the e)uatio! of the circle (hose radius is & ce!ter o! the li!e x =2 a!d ta!e!t to the li!e 3x – 4y + ## = 0.

    • A. $x – 2'2 + $y – 2'2 =

    • B. $x – 2'2 + $y + 2'2 = 2

    • C. $x – 2'2 + $y + 2'2 =

    • D. $x – 2'2 + $y – 2'2 = 2Problem 13:

    i!d the e)uatio! of the circle (ith the ce!ter at $%4& %' a!d ta!e!t to theli!e 2x + ,y – #0 = 0.

    • A. x2 + y2 + x – #0y – #2 = 0

    • B. x2 + y2 + x – #0y + #2 = 0

    • C. x2 + y2 + x + #0y – #2 = 0

    • D. x2 + y2 – x + #0y + #2 = 0Problem 14: ECE Board April 199i!d the "alue of 8 for (hich the e)uatio! x2 + y2 + 4x – 2y – 8 = 0 re5rese!tsa 5oi!t circle.

    A. • B. 6

    • C. %6

    • D. %Problem 15: ECE Board April 19993x2 + 2x – y + , = 0. Deteri!e the cur"e.

    • A. 9ara/ola

    • B. :lli5se

    • C. Circle

    • D. y5er/olaProblem 1!: CE Board May 1993% CE Board November 1993% ECEBoard April 1994 -he focus of the 5ara/ola y2 = #6x is at

    • A. $4& 0'

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    • B. $0& 4'

    • C. $3& 0'

    • D. $0& 3'Problem 1": CE Board November 1994

    Where is the "ertex of the 5ara/ola x2 = 4$y – 2'?• A. $2& 0'

    • B. $0& 2'

    • C. $3& 0'

    • D. $0& 3'Problem 1: ECE Board April 1994% ECE Board April 1999i!d the e)uatio! of the directrix of the 5ara/ola y 2 = #6x.

    • A. x = 2

    • B. x = %2

    • C. x = 4

    • D. x = %4Problem 19:;i"e! the e)uatio! of a 5ara/ola 3x + 2y2 – 4y + , = 0.

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    i!d the locatio! of the focus of the 5ara/ola y2 + 4x – 4y – = 0.

    • A. $2.& %2'

    • B. $3& #'

    • C. $2& 2'

    • D. $%2.& %2'Problem 23: ECE Board April 199i!d the e)uatio! of the axis of syetry of the fu!ctio! y = 2x2 – ,x + .

    • A. ,x + 4 = 0

    • B. 4x + , = 0

    • C. 4x – , = 0

    • D. x – 2 = 0Problem 24:

    A 5ara/ola has its focus at $,& %4' a!d directrix y = 2. i!d its e)uatio!.• A. x2 + #2y – #4x + 6# = 0

    • B. x2 – #4y + #2x + 6# = 0

    • C. x2 – #2x + #4y + 6# = 0

    • D. !o!e of the a/o"eProblem 25:

    A 5ara/ola has its axis 5arallel to the x%axis& "ertex at $%#& ,' a!d o!e e!d of

    the latus rectu at $%#14& 312'. i!d its e)uatio!.• A. y2 – ##y + ##x – 60 = 0

    • B. y2 – ##y + #4x – 60 = 0

    • C. y2 – #4y + ##x + 60 = 0

    • D. !o!e of the a/o"eProblem 2!: ECE Board November 199"Co5ute the focal le!th a!d the le!th of the latus rectu of the 5ara/olay2 + x – 6y + 2 = 0.

    • A. 2&

    B. 4& #6• C. #6& 64

    • D. #& 4Problem 2":;i"e! a 5ara/ola $y – 2'2 = $x – #'. What is the e)uatio! of its directrix?

    • A. x = %3

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    • B. x = 3

    • C. y = %3

    • D. y = 3Problem 2: ME Board #ctober 199"

     -he e!eral e)uatio! of a co!ic sectio! is i"e! /y the follo(i! e)uatio!Ax2 + Bxy + Cy2 + Dx + :y + = 0. A cur"e ay/e ide!tied as a! elli5se /y(hich of the follo(i! co!ditio!s?

    • A. B2 – 4AC @ 0

    • B. B2 – 4AC = 0

    • C. B2 – 4AC 0

    • D. B2 – 4AC = #Problem 29: CE Board November 1994What is the area e!closed /y the cur"e x2 + 2y2 – 22 = 0?

    • A. 4,.#

    • B. 0.2

    • C. 63.

    • D. ,2.3Problem 3$: ECE Board April 199

    9oi!t 9 $x& y' o"es (ith a dista!ce fro 5oi!t $0& #' o!e%half of its dista!cefro li!e y = 4. -he e)uatio! of its locus is?

    • A. 2x2 – 4y2 =

    • B. 4x2 + 3y2 = #2

    • C. 2x2 + y3 = 3• D. x2 + 2y2 = 4

    Problem 31:

     -he le!ths of the aor a!d i!or axes of a! elli5se are #0 a!d &res5ecti"ely. i!d the dista!ce /et(ee! the foci.

    • A. 3

    • B. 4

    • C.

    • D. 6Problem 32: -he e)uatio! 2x2 + #6y2 – #0x + #2y + # = 0 has its ce!ter at?

    • A. $3& %4'

    • B. $3& 4'

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    • C. $4& %3'

    • D. $3& 'Problem 33: EE Board #ctober 199"i!d the aor axis of the elli5se x2 + 4y2 – 2x – y + # = 0.

    • A. 2• B. #0

    • C. 4

    • D. 6Problem 34: CE Board May 1993

     -he le!th of the latus rectu for the elli5se is e)ual to?

    • A. 2

    • B. 3

    • C. 4

    • D. Problem 35:

    A! elli5se (ith a! ecce!tricity of 0.6 a!d has o!e of its foci 2 u!its fro thece!ter. -he le!th of the latus rectu is !earest to?

    • A. 3. u!its

    • B. 3. u!its

    • C. 4.2 u!its

    • D. 3.2 u!itsProblem 3!:

    A! earth satellite has a! a5oee of 40&000 8 a!d a 5eriee of 6&600 8.Assui! the radius of the earth as 6&400 8& (hat (ill /e the ecce!tricity

    of the elli5tical 5ath descri/ed /y the satellite (ith the ce!ter of the earth ato!e of the foci?

    • A. 0.46

    • B. 0.4

    • C. 0.2

    • D. 0.6

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    Problem 3": ECE Board April 199

     -he aor axis of the elli5tical 5ath i! (hich the earth o"es arou!d the su!is a55roxiately #6&000&000 iles a!d the ecce!tricity of the elli5se is#160. Deteri!e the a5oee of the earth.

    • A. 3&000&000 iles

    • B. #&40&000 iles

    • C. 4&33 iles

    • D. 4&0&000 ilesProblem 3: CE Board November 1992

     -he earths or/it is a! elli5se (ith the su! at o!e of the foci. f the farthestdista!ce of the su! fro the earth is #0. illio! 8 a!d the !earest

    dista!ce of the su! fro the earth is ,.2 illio! 8& !d the ecce!tricity of the elli5se.

    • A. 0.#

    • B. 0.2

    • C. 0.3

    • D. 0.4Problem 39:

    A! elli5se (ith ce!ter at the orii! has a le!th of aor axis 20 u!its. f the

    dista!ce fro ce!ter of elli5se to its focus is & (hat is the e)uatio! of itsdirectrix?

    • A. x = #

    • B. x = 20

    • C. x = #

    • D. x = #6Problem 4$:What is the le!th of the latus rectu of 4x2 + y2 + x – 32 = 0?

    • A. 2.• B. 2.,

    • C. 2.3

    • D. 2.Problem 41: EE Board #ctober 19934x2 – y2 = #6 is the e)uatio! of a1a!?

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    • A. 5ara/ola

    • B. hy5er/ola

    • C. circle

    • D. elli5seProblem 42: EE Board #ctober 1993i!d the ecce!tricity of the cur"e x2 – 4y2 – 36x + y = 4.

    • A. #.0

    • B. #.2

    • C. #.6

    • D. #.,6Problem 43: CE Board November 1995o( far fro the x%axis is the focus of the hy5er/ola x2 – 2y2 + 4x + 4y + 4

    = 0?• A. 4.

    • B. 3.4

    • C. 2.,

    • D. 2.#Problem 44: EE Board #ctober 1994

     -he sei%tra!s"erse axis of the hy5er/ola is?

    • A. 2

    • B. 3

    • C. 4

    • D. Problem 45: CE Board May 199!

    What is the e)uatio! of the asy5tote of the hy5er/ola?

    • A. 2x – 3y = 0

    • B. 3x – 2y = 0

    • C. 2x – y = 0

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    • D. 2x + y = 0Problem 4!: EE Board April 1994

    i!d the e)uatio! of the hy5er/ola (hose asy5totes are y = 2x a!d(hich 5asses throuh $12& 3'.

    • A. 4x2 + y2 + #6 = 0• B. 4x2 + y2 – #6 = 0

    • C. x2 – 4y2 – #6 = 0

    • D. 4x2 – y2 = #6Problem 4":

    i!d the e)uatio! of the hy5er/ola (ith "ertices $%4& 2' a!d $0& 2' a!d foci $%&2' a!d $#& 2'.

    • A. x2 – 4y2 + 20x +#6y – #6 = 0

    • B. x2 – 4y2 + 20x – #6y – #6 = 0

    • C. x2 – 4y2 – 20x +#6y + #6 = 0• D. x2 + 4y2 – 20x +#6y – #6 = 0

    Problem 4:i!d the dista!ce /et(ee! 9# $6& %2& %3' a!d 92 $& #& %4'.

    Problem 49:

     -he 5oi!t of i!tersectio! of the 5la!es x + y – 2E = F 3x – 2y + E = 3 a!d x+ y + E = 2 is at?

    • A. $2& #& %#'

    • B. $2& 0& %#'

    • C. $%#& #& %#'

    • D. $%#& 2& %#'Problem 5$: ME Board April 199"

    What is the radius of the s5here ce!ter at the orii! that 5asses the 5oi!t &#& 6?

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    Problem 51:

     -he e)uatio! of a s5here (ith ce!ter at $%3& 2& 4' a!d of radius 6 u!its is?• A. x2 + y2 + E2 +6x – 4y – E = 36

    • B. x2 + y2 + E2 +6x – 4y – E = ,

    • C. x2 + y2 + E2 +6x – 4y + E = 6

    • D. x2 + y2 + E2 +6x – 4y + E = 36Problem 52: EE Board April 199"

    i!d the 5olar )uestio! of the circle& if its ce!ter is at $4& 0' a!d the radius 4.

    • A. r – cos G = 0

    • B. r – 6 cos G = 0

    • C. r – #2 cos G = 0

    • D. r – 4 cos G = 0Problem 53: ME Board #ctober 199!What are the x a!d y coordi!ates of the focus of the ico!ic sectio! descri/ed/y the follo(i! e)uatio!? $A!le G corres5o!ds to a riht tria!le (ithadace!t side x& o55osite side y a!d the hy5ote!use r.' r &in2 ' ( co& '

    • A. $#14& 0'

    • B. $0& 712'

    • C. $0& 0'

    • D. $%#12& 0'Problem 54:

    i!d the 5olar e)uatio! of the circle of radius 3 u!its a!d ce!ter at $3& 0'.

    • A. r = 3 cos G

    • B. r = 3 si! G

    • C. r = 6 cos G

    • D. r = si! GProblem 55: EE Board #ctober 199"

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    ;i"e! the 5olar e)uatio! r = si! G. Deteri!e the recta!ular coordi!ate$x& y' of a 5oi!t i! the cur"e (he! G is 30H.

    • A. $2.#,& #.2'

    • B. $3.0& #.'

    • C. $2.#& 4.#2'

    • D. $6& 3'

    #. -he "ertex of the 5ara/ola y2 – 2x + 6y + 3 = 0 is at

    • A. $%3& 3'

    • B. $3& 3'

    • C. $%3& 3'

    • D. $%3& %3'

    2. -he le!th of the latus rectu of the 5ara/ola y2 = 45x is

    • A. 45

    • B. 25

    • C. 9

    • D. %453. ;i"e! the e)uatio! of the 5ara/ola y2 – x – 4y – 20 = 0. -he le!th ofits latus rectu is

    • A. 2

    • B. 4

    • C. 6

    • D. 4. What is the le!th of the latus rectu of the cur"e x2 = –#2y?

    • A. #2

    • B. %3

    • C. 3

    • D. %#2. i!d the e)uatio! of the directrix of the 5ara/ola y 2 = 6x.

    • A. x =

    • B. x = 4

    • C. x = %

    • D. x = %4

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    6. -he cur"e y = –x2 + x + # o5e!s

    • A. >5(ard

    • B. -o the left

    • C. -o the riht

    • D. Do(!(ard,. -he 5ara/ola y = –x2 + x + # o5e!s

    • A. -o the riht

    • B. -o the left

    • C. >5(ard

    • D. Do(!(ard. i!d the e)uatio! of the axis of syetry of the fu!ctio! y = 2x2 – ,x +.

    • A. 4x + , = 0

    • B. x – 2 = 0

    • C. 4x – , = 0

    • D. ,x + 4 = 0

    . i!d the e)uatio! of the locus of the ce!ter of the circle (hich o"es sothat it is ta!e!t to the y%axis a!d to the circle of radius o!e $#' (ith ce!terat $2&0'.

    A. x2

     + y2

     – 6x + 3 = 0• B. x2 – 6x + 3 = 0

    • C. 2x2 + y2 – 6x + 3 = 0

    • D. y2 – 6x + 3 = 0

    60. i!d the e)uatio! of the 5ara/ola (ith "ertex at $4& 3' a!d focus at $4&%#'.

    • A. y2 – x + #6y – 32 = 0

    • B. y2 + x + #6y – 32 = 0

    • C. y2 + x – #6y + 32 = 0

    • D. x2 – x + #6y – 32 = 06#. i!d the area /ou!ded /y the cur"es x2 + y + #6 = 0& x – 4 = 0& the x%axis& a!d the y%axis.

    • A. #0.6, s). u!its

    • B. #0.33 s). u!its

    • C. .6, s). u!its

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    • D. s). u!its62. i!d the area $i! s). u!its' /ou!ded /y the 5ara/olas x 2 – 2y = 0 a!dx2 + 2y – = 0

    • A. ##.,

    • B. #0.,• C. .,

    • D. 4.,63. -he le!th of the latus rectu of the cur"e $x – 2'2 1 4 = $y + 4'2 1 2 = #is

    • A. #.6

    • B. 2.3

    • C. 0.0

    • D. #.2

    64. i!d the le!th of the latus rectu of the follo(i! elli5se2x2 + y2 – 300x –#44y + #2# = 0

    • A. 3.4

    • B. 3.2

    • C. 3.6

    • D. 3.0

    6. f the le!th of the aor a!d i!or axes of a! elli5se is #0 c a!d c&res5ecti"ely& (hat is the ecce!tricity of the elli5se?

    • A. 0.0

    • B. 0.60

    • C. 0.,0

    • D. 0.066. -he ecce!tricity of the elli5se x214 + y2 1 #6 = # is

    • A. 0.,2• B. 0.26

    • C. 0.6

    • D. 0.666,. A! elli5se has the e)uatio! #6x2 + y2 + 32x – #2 = 0. ts ecce!tricity is

    • A. 0.3#

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    • B. 0.66

    • C. 0.24

    • D. 0.36. -he ce!ter of the elli5se 4x2 + y2 – #6x – 6y – 43 = 0 is at

    • A. $2& 3'

    • B. $4& %6'

    • C. $#& '

    • D. $%2& %'

    6. i!d the ratio of the aor axis to the i!or axis of the elli5sex2 + 4y2 – ,2x – 24y – #44 = 0

    • A. 0.6,

    • B. #.

    • C. #.

    • D. 0.,,0. -he area of the elli5se x2 + 2y2 – 36x – # = 0 is e)ual to

    • A. #7 s). u!its

    • B. 207 s). u!its

    • C. 27 s). u!its

    • D. 307 s). u!its,#. -he area of the elli5se is i"e! as A = 3.#4#6 a /. i!d the area of theelli5se 2x2 + #6y2 – #00x + 32y = 24

    • A. 6.2 s)uare u!its

    • B. 62. s)uare u!its

    • C. 6.2 s)uare u!its

    • D. 2.6 s)uare u!its

    ,2. -he sei%aor axis of a! elli5se is 4 a!d its sei%i!or axis is 3. -hedista!ce fro the ce!ter to the directrix is

    • A. 6.32

    • B. 6.04,

    • C. 0.66#4

    • D. 6.222

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    ,3. ;i"e! a! elli5se x2 1 36 + y2 1 32 = #. Deteri!e the dista!ce /et(ee!foci.

    • A. 2

    • B. 3

    • C. 4

    • D. ,4. o( far a5art are the directrices of the cur"e 2x2 + y2 – 300x – #44y +#2# = 0?

    • A. #2.

    • B. #4.2

    • C. #3.2

    • D. #.2

    ,. -he aor axis of the elli5tical 5ath i! (hich the earth o"es arou!d thesu! is a55roxiately #6&000&000 iles a!d the ecce!tricity of the elli5se is#160. Deteri!e the a5oee of the earth.

    • A. 4&0&000 iles

    • B. 4&33.#00 iles

    • C. #&40&000 iles

    • D. 3&000&000 iles

    ,6. i!d the e)uatio! of the elli5se (hose ce!ter is at $%3& %#'& "ertex at $2&%#'& a!d focus at $#& %#'.

    • A. x2 + 36y2 – 4x + 0y – ##6 = 0

    • B. 4x2 + 2y2 + 4x – 0y – #22 = 0

    • C. x2 + 2y2 + 0x + 0y + #0 = 0

    • D. x2 + 2y2 + 4x + 0y – ## = 0

    ,,. 9oi!t 9$x& y' o"es (ith a dista!ce fro 5oi!t $0& #' o!e%half of itsdista!ce fro li!e y = 4& the e)uatio! of its locus is

    • A. 4x2 + 3y2 = #2• B. 2x2 % 4y2 =

    • C. x2 + 2y2 = 4

    • D. 2x2 + y3 = 3

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    ,. -he chords of the elli5se 64I2 + 2yI2 = #600 ha"i! e)ual slo5es of#1 are /isected /y its diaeter. Deteri!e the e)uatio! of the diaeter ofthe elli5se.

    • A. x – 64y = 0

    B. 64x – y = 0• C. x +64y = 0

    • D. 64x + y = 0,. i!d the e)uatio! of the u5(ard asy5tote of the hy5er/ola (hosee)uatio! is $x – 2'2 1 – $y + 4'2 1 #6

    • A. 3x + 4y – 20 = 0

    • B. 4x – 3y – 20 = 0

    • C. 4x + 3y – 20 = 0

    • D. 3x – 4y – 20 = 00. -he sei%co!uate axis of the hy5er/ola $x21' – $y214' = # is

    • A. 2

    • B. %2

    • C. 3

    • D. %3#. What is the e)uatio! of the asy5tote of the hy5er/ola $x 21' – $y214' = #.

    • A. 2x – 3y = 0

    • B. 3x – 2y = 0

    • C. 2x – y = 0

    • D. 2x + y = 0

    2. -he ra5h y = $x – #' 1 $x + 2' is !ot de!ed at

    • A. 0

    • B. 2

    C. %2• D. #

    3. -he e)uatio! x2 + Bx + y2 + Cy + D = 0 is

    • A. y5er/ola

    • B. 9ara/ola

    • C. :lli5se

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    • D. Circle4. -he e!eral seco!d deree e)uatio! has the for Ax2 + Bxy + Cy2 + Dx+ :y + = 0 a!d descri/es a! elli5se if

    • A. B2 – 4AC = 0

    • B. B2 – 4AC 0

    • C. B2 – 4AC = #• D. B2 – 4AC @ 0

    . i!d the e)uatio! of the ta!e!t to the circle x 2 + y2 – 34 = 0 throuh5oi!t $3& '.

    • A. 3x + y %34 = 0

    • B. 3x – y – 34 = 0

    • C. 3x + y + 34 = 0

    • D. 3x – y + 34 = 0

    6. i!d the e)uatio! of the ta!e!t to the cur"e x2

     + y2

     + 4x + #6y – 32 = 0throuh $4& 0'.

    • A. 3x – 4y + #2 = 0

    • B. 3x – 4y – #2 = 0

    • C. 3x + 4y + #2 = 0

    • D. 3x + 4y % #2 = 0,. i!d the e)uatio! of the !oral to the cur"e y2 + 2x + 3y = 0 thouh5oi!t $%&2'

    • A. ,x + 2y + 3 = 0

    • B. ,x % 2y + 3 = 0

    • C. 2x % ,y % 3 = 0

    • D. 2x + ,y % 3 = 0. Deteri!e the e)uatio! of the li!e ta!e!t to the ra5h y = 2x2 + #& atthe 5oi!t $#& 3'.

    • A. y = 4x + #

    • B. y = 4x – #

    C. y = 2x – #• D. y = 2x + #

    . i!d the e)uatio! of the ta!e!t to the cur"e x 2 + y2 = 4# throuh $& 4'.

    • A. x + 4y = 4#

    • B. 4x – y = 4#

    • C. 4x + y = 4#

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    • D. x – 4y = 4#0. i!d the e)uatio! of a li!e !oral to the cur"e x2 = #6y at $4& #'.

    • A. 2x – y – = 0

    • B. 2x – y + =

    • C. 2x + y – = 0

    • D. 2x + y + = 0#. What is the e)uatio! of the ta!e!t to the cur"e x2 + 2y2 – 22 = 0 at$0& 3'?

    • A. y + 3 = 0

    • B. x + 3 = 0

    • C. x – 3 = 0

    • D. y – 3 = 0

    2. What is the e)uatio! of the !oral to the cur"e x2 + y2 = 2 at $4& 3'?

    • A. 3x – 4y = 0

    • B. x + 3y = 0

    • C. x – 3y = 0

    • D. 3x + 4y = 0

    3. -he 5olar for of the e)uatio! 3x + 4y – 2 = 0 is

    • A. 3r si! J + 4r cos J = 2

    • B. 3r cos J + 4r si! J = %2

    • C. 3r cos J + 4r si! J = 2

    • D. 3r si! J + 4r ta! J = %2

    4. -he 5olar for of the e)uatio! 3x + 4y – 2 = 0 is• A. r2 =

    • B. r = J1$cos2 J + 2'

    • C. r =

    • D. r2 = 1$cos2 J + 2'

    . the dista!ce /et(ee! 5oi!ts $& 30K' a!d $%& %0K' is

    • A. .4

    • B. #0.#4

    • C. 6.#3

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    • D. #2.#4

    6. Co!"ert J = 713 to Cartesia! e)uatio!.

    • A. x = L3 x

    • B. y = x

    • C. 3y = L3 x

    • D. y =L3 x

    ,. -he 5oi!t of i!tersectio! of the 5la!es x + y – 2E = & 3x – 2y + E = 3&a!d x + y + E = 2 is

    • A. $2& #& %#'

    • B. $2& 0& %#'

    • C. $%#& #& %#'

    • D. $%#& 2& #'

    . A (arehouse roof !eeds a recta!ular s8yliht (ith "ertices $3& 0& 0'& $3&3& 0'& $0& 3& 4'& a!d $0& 0& 4'. f the u!its are i! eter& the area of the s8ylihtis

    • A. #2 s). .

    • B. 20 s). .

    • C. # s). .• D. s). .

    . -he dista!ce /et(ee! 5oi!ts i! s5ace coordi!ates are $3& 4& ' a!d $4& 6&,' is

    • A. #

    • B. 2

    • C. 3

    • D. 4

    #00. What is the radius of the s5here (ith ce!ter at orii! a!d (hich 5assesthrouh the 5oi!t $& #& 6'?

    • A. #0

    • B.

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    • C.L#0#

    • D. #0.