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Assignment: Pair of Straight Lines Date: 29thJanuary. 2010 Batch: Target

1. Find the differences of the tangents of the angles which the lines 0sintan2)cos(tan 22222 =++ yxyx

make with the x-axis.

2. ro!e that the e"#ations 0$$ 2$2$ =+ yxyxyx re%resents the three lines are e"#all& inclined to each

other.

$. Find the condition so that the %air of straight line 'oining the origin to the intersections of the line cmxy +=

and the circle 222 ayx =+ is at the right angles.

. et * +e the origin and ),( P where ( )dxxxandx

xofvalueleast =

+

=

1

12

2

-.1

1 . Find the !al#e of

*.

/. traight lines ++=+= Rmwherecmxyandcmxy 21 , meets the x-axis at 21 AandA res%. and &-axis at

21 BandB res%. t is gi!en that %oints 2121 ,, BandBAA are conc&clic. Find the loc#s of intersection of lines

1221 BAandBA .

. et g(x) +e a f#nction defined in (-1, 1). f the area of the e"#ilateral triangle with two of its !ertices at (0, 0)

and 3x, g(x)4 is

$, find the f#nction g(x).

5. f the straight lines 0222 22 =+++++ cfygxbyhxyax intersects on the x-axis. Find the condition +etween

constants.

6. f one of the lines of the %air 02 22 =++ byhxyax +isects the angle +etween %ositi!e directions of the axes, Find

the condition +etween a, +, and h.

7. Find the !al#e of for which the lines 'oining the %oint of intersection of c#r!es 21 CandC to the origin are

e"#all& inclined to the x-axis, 0$6$:072$: 22222

1 =+=++ xxyyxCandxxyyxC

10. 8he cartesian co-ordinates (x, &) of a %oint on a c#r!e are gi!en +& 1:$:1:: 2$ = tttyx where t is a

%arameter, then the %oints gi!en +& cbat ,,= are collinear.

11. f banda are %ositi!e n#m+er )( ba < , Find the range of !al#es of 9; for which a real +e fo#nd s#ch

that the e"#ation 0)1(22 22 =+++++ yxKbyxyax re%resents a %air of straight lines.

12.

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1/. f 0222 22 =+++++ cfygxbyhxyax re%resents a %air of straight lines, e"#idistant from the origin, then %ro!e

that )( 22 agbfcgf =