Center @ (-2, 1)r2 = 16r = 4

44

4

4

Center @ (0, 0)r2 = 25r = 5

55

5

5

222

222

543

cba

43

434

3

5

Special Pythagorean Triple

(___, 0)Substitute in 0 for y and solve for x.

16102 22 x 1612 2 x

152 2 x

152 x

152 x

0,152

0,152;0,152

(0, ___)Substitute in 0 for x and solve for y.

16120 22 y 1614 2 y

121 2 y121 y

321y

321,0

321,0;321,0

( h, k ) ( x, y )

222 rkyhx Substitute in h and k as 1 and -2.

222

222

21

21

ryx

ryx

Substitute in x and y as 4 and 2.

222 2214 r Solve for r2.

2

222

25169

43

r

r

222 21 ryx

2521 22 yx

022 cbyaxyxGENERAL FORM OF THE EQUATION OF A CIRCLE:

096422 yxyxGraph 222 rkyhx Convert to by completing the square. Group x terms and y terms together

and move the constant to the other side.964 22 yyxx

Complete the square of the x’s and y’s. ______9___6___4 22 yyxx

yx yx

432 22 yx

94 (+2)2 (-3)2

Center @ (-2, 3) r2 = 4r = 2

Graph 02481222 22 yxyxDivide everything by 2. Why?

0124622 yxyx ______12___4___6 22 yyxx

yx yx 2523 22 yx

49 (-3)2 (-2)2

Center @ (3, 2) r2 = 25r = 5

Focus

Directrix

-a

a

-a

yx xa y (-a)0 x

2222 0 ayayx Square both sides to remove radical.

22

222 ayayx FOIL the binomials.

22222 22 aayyaayyx

Cancel like terms on each side.ayayx 222

Solve for x2.

ayx 42

a

a2a2a2a

4a4a

Graph the following equations.

xy 122 The y is squared and the coefficient on the x is positive, the parabola opens to the right. 4a = 12, a = 3 and the vertex is at (0, 0).

6

F

6

V 3

x = - 3

Graph the following equations.

yx 162 The x is squared and the coefficient on the y is negative, the parabola opens down. 4a = -16, a = -4 and the vertex is at (0, 0).

8F 8

4

V

y = 4

Graph the following equations.

xy 82 The y is squared and the coefficient on the x is negative, the parabola opens to the left. 4a = -8, a = -2 and the vertex is at (0, 0).

4

F 4

V 2

x = 2

Graph the following equations.

182 2 yx The x is squared and the coefficient on the y is positive, the parabola opens up. 4a = 8, a = 2 and the vertex is at (2, -1).

4 F 4

V

2

y = - 3

Graph the following equations.

017422 xyy We need to complete the square of the y-terms to put in graphing form. Isolate the y-terms.

___174___22 xyy 1(-1)2

1641 2 xy Factor out the 4 as the GCF.

441 2 xy The y is squared and the coefficient on the x is positive, the parabola opens to the right. 4a = 4, a = 1 and the vertex is at (4, 1).

2

2V F

x = 3

Graph the following equations.01462 yxx

2

V

2F

We need to complete the square of the x-terms to put in graphing form. Isolate the x-terms.

___14___62 yxx 9(+3)2

843 2 yx Factor out the 4 as the GCF.

243 2 yx The x is squared and the coefficient on the y is positive, the parabola opens up. 4a = 4, a = 1 and the vertex is at (-3, -2).

y = - 3

Draw a rough graph.

(2,3)

Equation format is ...axy 42

…plug in x & y to solve for 4a. 243 2 a

a

a

429

249

xy292

Draw a rough graph.

V F

Equation format is ... hxaky 42

…distance from V to F is 1, a = 1, and plug in the vertex values.

1142 2 xy 142 2 xy

Draw a rough graph.F(-4, 4)

Equation format is ...

kyahx 42

1344 2 yx 1124 2 yx

V(-4, ?)

y = -2

…distance from F to the directrix line is 6, V is halfway, so a = 3. Plug in a and the vertex values.

4 – 3 = 1V(-4, 1)

3