section 10.1 – the circle write the standard form of each equation. then graph the equation....
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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
h, kCenter : Radius : r
center (0, 3) and radius 2
h = 0, k = 3, r = 2
2 2 2x y 20 3
22x y 3 4
Write the standard form of each equation. Then graph the equation.
2 2 2x y rh k
h, kCenter : Radius : r
center (-1, -5) and radius 3
h = -1, k = -5, r = 3
2 2 231 5x y
2 2x 1 y 5 9
Write the standard form of each equation. Then graph the equation.
2 2 2x y rh k
h, kCenter : Radius : r
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
Write the standard form of each equation. Then graph the equation.
2 2 2x y rh k
h, kCenter : Radius : r
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
Write the standard form of each equation. Then graph the equation.
2 2 2x y rh k
h, kCenter : Radius : r
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
b) Provide the appropriate information.
Focus: (4, 2)Vertex: (2, 2)
Directrix: x = 0Axis of Sym: y = 2
c) Graph the equation
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
b) Provide the appropriate information.
Focus: (3, 0)Vertex: (3, 2)
Directrix: y = 4Axis of Sym: x = 3
c) Graph the equation
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
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