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Section 10.1 – The Circle

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

center (0, 3) and radius 2 h = 0, k = 3, r = 2

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

center (-1, -5) and radius 3 h = -1, k = -5, r = 3

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

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

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

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**Find the equation of the circle with center (8, -9) and passes**

through the point (21, 22).

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

through the origin

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**Find the equation of the circle whose endpoints of a diameter**

are (11, 18) and (-13, -20) Center is the midpoint of the diameter Radius uses distance formula

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**Find the equation of the circle tangent to the y-axis and**

center of (-8, -7). r = 8 C

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**Find the equation of the circle whose center is in the first**

quadrant, and is tangent to x = -3, x = -5, and the x-axis r = 4 x x

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Section 10.2 – The Parabola Opens Left/Right Opens Up/Down Vertex: (h, k) Vertex: (h, k) Focus: Focus: Directrix: Directrix: Axis of Sym: Axis of Sym:

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F 2p p 2p V p Directrix

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Directrix 2p F p V p 2p

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Given the equation a) Write the equation in standard form b) Provide the appropriate information. Focus: (0, 2) Vertex: (0, 0) Directrix: y = -2 Axis of Sym: x = 0 F c) Graph the equation V

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Given the equation a) Write the equation in standard form

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Given the equation a) Write the equation in standard form b) Provide the appropriate information. Focus: (4, 2) Vertex: (2, 2) Directrix: x = 0 Axis of Sym: y = 2 F V c) Graph the equation

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Given the equation a) Write the equation in standard form

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Given the equation a) Write the equation in standard form b) Provide the appropriate information. V Focus: (3, 0) Vertex: (3, 2) Directrix: y = 4 Axis of Sym: x = 3 F c) Graph the equation

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**Write the equation of the parabola with focus at (2, 2)**

and directrix x = 4 F V

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

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**Write the equation of the parabola with axis of symmetry y = 2,**

directrix x = 4, and p = -3 F V

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Section 10.3 – The Ellipse a > b a – semi-major axis b – semi-minor axis C(h, k) V1(h + a, k), V2(h – a, k) F1(h + c, k), F2(h – c, k) C(h, k) V1(h, k + a), V2(h, k – a) F1(h, k + c), F2(h, k – c)

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V1 V2 a F1 F2 c b C C(1, 4) V(1, -1), (1, 9) F(1, 0), (1, 8)

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b c c V1 V2 a F1 F2 C C(-1, -2) V(-9, -2), (8, -2) F(-6.7, -2), (4.7, -2)

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V1 V2 F1 F2 C C(0, 0) V(-4, 0), (4, 0) F(-2.6, 0), (2.6, 0)

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Now graph it………

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V1 V2 F1 F2 C C(-3, 1) V(-7, 1), (1, 1) F(-5, -1), (-1, 1)

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**Find the equation of the ellipse whose center is at (2, -2), vertex**

at (7, -2) and focus at (4, -2). C(2, -2) a = 5 c = 2 C F V

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

and focus at (4, 8) C(4, 6) a = 3 c = 2 V F C V

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**Find the equation of the ellipse whose foci are (5, 1) and (-1, 1),**

and length of the major axis is 8 C(2, 1) c = 3 Major is 8 Semi-major is 4 a = 4 F C F

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Conics Review Study Hard!. Name the Conic without graphing and write it in standard form X 2 + Y 2 -4Y-12=0.

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