section 10.1 – the circle write the standard form of each equation. then graph the equation....

Section 10.1 – The Circle

2 2 2x y rh k

h, kCenter : Radius : r

Write the standard form of each equation. Then graph the equation.

2 2 2x y rh k


center (0, 3) and radius 2

h = 0, k = 3, r = 2

2 2 2x y 20 3

22x y 3 4


2 2 2x y rh k


center (-1, -5) and radius 3

h = -1, k = -5, r = 3

2 2 231 5x y

2 2x 1 y 5 9


2 2 2x y rh k


2 2x y 4x 9

22x 4x y 9

22 4 4x 4x y 9

22 2x y 32 1

2 2x 2 y 13

-2, Center: Radius0 : 13


2 2 2x y rh k


2 2x y 6y 50 14x

2 2x 14x y 6y 50

2 2x 14x y 6y 5049 9 49 9

22 2108y7x 3

2 2x 7 y 3 108

-7, -Center: Radius:3 108


2 2 2x y rh k


2 2x y 18x 18y 53 0

2 2x 18x y 18y 53

2 2x 18x y 1881 81 81 8y 3 15

22 29 9 1 9x 0y

2 2x 9 y 9 109

9, 9Center: Radius: 109

2 24x 4y 36x 5 0

2 24x 36x 4y 5

2 24 x 9x 4 y 5

2 2x 9x 481 81

4 44 4

y 5

2

294 x 4 y 76

2

2

29

4 x 4 y 7624 4 4

2

229

2x y 19

-9

, 1Center: Radius: 9 02

2 23x 3y 6x 1

2 23x 6x 3y 1

2 23 x 2x 3 y 1

22x 2x 3 y 1 33 1

2 23 x 1 3 y 4

2

2 2 4x 1 y

3

-1, Center: Radius0 :

4

3

2 23 x 1 3 y 4

3 3 3

2 22x 2y 28x 12y 114 0

2 22x 28x 2y 12y 114

2 22 x 14x 2 y 6y 114

2 2x 14x y 6y2 49 2 9 911 184 8

2 22 x 7 2 y 3 2

7, -Center: Radius3 : 1

2 2x y7 3 1

Find the equation of the circle with center (8, -9) and passes through the point (21, 22).

2 2 2x y rh k

2 2 2x 8 y 9 r

2 2 221 8 22 9 r 21130 r

2 2x 8 y 9 1130

Find the equation of the circle with center (-13, 42) and passes through the origin

2 2 2x y rh k

2 2 2x 13 y 42 r

2 2 20 13 0 42 r 21933 r

2 2x 13 y 42 1933

Find the equation of the circle whose endpoints of a diameterare (11, 18) and (-13, -20)

Center is the midpoint of the diameter

11 13 18 20, 1 1,

2 2

Radius uses distance formula

2 2

1 2 1 2r x x y y

2 2r 11 1 18 1

r 505

2 2r 13 1 20 1

r 505

22 21 1 05x 5y

Find the equation of the circle tangent to the y-axis and center of (-8, -7).

Cr = 8

2 2 28 8x y 7

Find the equation of the circle whose center is in the firstquadrant, and is tangent to x = -3, x = -5, and the x-axis

x

x r = 4

2 2 2x y 41 4

Section 10.2 – The Parabola

2y 4k hxp 2

x 4h kyp

Vertex: (h, k)

Opens Left/Right Opens Up/Down

Vertex: (h, k)

Focus: h k2p, Focus: h, k 2p

Directrix: x 2h p Directrix: y 2k p

Axis of Sym: y k Axis of Sym: x h

V

p

2p2pF

p

Directrix

Vp

2p

2p

Fp

Directrix

Given the equation 2x 8ya) Write the equation in standard form

2x 4h kyp 2

x y0 024

V

F

b) Provide the appropriate information.

Focus: (0, 2)Vertex: (0, 0)

Directrix: y = -2Axis of Sym: x = 0

c) Graph the equation

Given the equation 2y 8x 4y 20 0 a) Write the equation in standard form

2y 4y 8x 20 2 4 4y 4y 8x 20

2y 82 x 16

22x2y 8

2y 42 2x2

Given the equation 2y 8x 4y 20 0 a) Write the equation in standard form

2y 4y 8x 20 2y x2 224

V

F



Directrix: x = 0Axis of Sym: y = 2


Given the equation 2x 6x 8y 7 0 a) Write the equation in standard form

2x 6x 8y 7 2 9 9x 6x 8y 7

2y 63x 8 1

2283x y

2x 43 y2 2

Given the equation 2x 6x 8y 7 0 a) Write the equation in standard form

2x 6x 8y 7 0 2x 43 2y2

V

F



Directrix: y = 4Axis of Sym: x = 3


Write the equation of the parabola with focus at (2, 2)and directrix x = 4

F

V

2y 4k hxp

2y 42 x1 3

242 3y x

Write the equation of the parabola with V(-1, -3) and F(-1, -6)

V

F

2x 4h kyp

2x 4 31 3y

221 3x y1

Write the equation of the parabola with axis of symmetry y = 2, directrix x = 4, and p = -3

V

F

2y 4k hxp

2y 42 x3 1

222 1y x1

Section 10.3 – The Ellipse

2 2 2 2

2 2 2 2

x y x

a b

y1 1

h h k

b a

k

a > ba – semi-major axisb – semi-minor axis

2 2 2a b c

C(h, k)V1(h + a, k), V2(h – a, k)F1(h + c, k), F2(h – c, k)

22: left/right fr

aLR

bom F

C(h, k)V1(h, k + a), V2(h, k – a)F1(h, k + c), F2(h, k – c)

22: up/down fr

b

aLR om F

2 2x y

19 5

1 4

2

2 2 2

a

a b

5

b 3

c

225 9 c

c 4

2b 9

1.8a 5

C

V1

V2

a

a

b b

F1

F2

c

c

C(1, 4)V(1, -1), (1, 9)F(1, 0), (1, 8)

2 2x y1 2

1 41

8 9

2 2 2

a

a b

9

b 7

c

281 49 c

c 5.7

2b 49

5.4a 9

CV1 V2aa

b

b

F1 F2cc

C(-1, -2)V(-9, -2), (8, -2)

F(-6.7, -2), (4.7, -2)

2 2x y1

16 9

2 2 2

a

a b

4

b 3

c

21

c 2 6

6 9 c

.

2b 92.3

a 4

CV1 V2F1 F2

C(0, 0)V(-4, 0), (4, 0)

F(-2.6, 0), (2.6, 0)

2 29x 25y 36x 50y 164 0 2 225y9x 36 4x 1650y

2 225 y9 x 4 164x 2y

2 225 y 2y 19 16x 4x 4 5364 2

2 225 y 19 x 2252

2 2259 y 1x 225

225 225 22

2

5

2 2x y2 1

125 9

2 264x 16y 288y 272 0 22 26 16y 24x 788y 2

2 216 y 1 2764x 8y 2

2 216 y 18y 81 1296264x 27

2 216 y 9x 26 04 1 4

226 1024

1024 1

16 y4 9

0 024

x

24 1

2 2x y0 9

6 61

1 4

2 212x 16y 72x 32y 68 0 2 21612 y 68x 7 y2x 32

2 21612 y yx 6 68x 2

2 21612 x 6 y 2y 1 1x 9 1088 66

2 216 y 191 x 23 12

2 21612 x 3 192

192 19

y 1

2 192

2 2x y3 1

6 11

1 2

Now graph it………

2 2x y3 1

6 11

1 2

2 2 2

a 4

b 12 3.

a b

5

c

216 12

2

c

c

2b 12

3a 4

CV1 V2F1 F2

C(-3, 1)V(-7, 1), (1, 1)

F(-5, -1), (-1, 1)

Find the equation of the ellipse whose center is at (2, -2), vertex at (7, -2) and focus at (4, -2).

C F V

C(2, -2)

a = 5

c = 22 2 2

2 2 2

2

a b c

5 b 2

b 21

2 2x 2 y 2

125 21

Find the equation of the ellipse with vertices at (4, 3) and (4, 9) ,and focus at (4, 8)

V

V

C

C(4, 6)a = 3

F

c = 22 2 2

2 2 2

2

a b c

3 b 2

b 5

2 2x 4 x 6

15 9

Find the equation of the ellipse whose foci are (5, 1) and (-1, 1),and length of the major axis is 8

FF C

C(2, 1)c = 3

Major is 8Semi-major is 4

a = 4

2 2 2

2 2 2

2

a b c

4 b 3

b 7

2 2x 2 y 1

116 7

section 10.1 – the circle write the standard form of each equation. then graph the equation....

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