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Section 10.1 – The Circle 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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Presentation on theme: "Section 10.1 – The Circle Write the standard form of each equation. Then graph the equation. center (0, 3) and radius 2 h = 0, k = 3, r = 2."— Presentation transcript:

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2 Section 10.1 – The Circle

3 Write the standard form of each equation. Then graph the equation. center (0, 3) and radius 2 h = 0, k = 3, r = 2

4 Write the standard form of each equation. Then graph the equation. center (-1, -5) and radius 3 h = -1, k = -5, r = 3

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

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

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

13 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

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

15 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 x x r = 4

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

17 V p 2p F p Directrix

18 V p 2p F p Directrix

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

20 Given the equation a) Write the equation in standard form

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

22 Given the equation a) Write the equation in standard form

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

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

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

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

27 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)

28 CV1 V2 a a bb F1 F2 c c C(1, 4) V(1, -1), (1, 9) F(1, 0), (1, 8)

29 C V1V2 aa b b F1 F2 cc C(-1, -2) V(-9, -2), (8, -2) F(-6.7, -2), (4.7, -2)

30 CV1V2 F1 F2 C(0, 0) V(-4, 0), (4, 0) F(-2.6, 0), (2.6, 0)

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33 Now graph it………

34 C V1V2 F1 F2 C(-3, 1) V(-7, 1), (1, 1) F(-5, -1), (-1, 1)

35 Find the equation of the ellipse whose center is at (2, -2), vertex at (7, -2) and focus at (4, -2). CF V C(2, -2) a = 5 c = 2

36 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 = 2

37 Find the equation of the ellipse whose foci are (5, 1) and (-1, 1), and length of the major axis is 8 FFC C(2, 1) c = 3 Major is 8 Semi-major is 4 a = 4


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