Section 10.1 – The Circle. Section 10.1 – The Circle.

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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:

F 2p p 2p V p Directrix

Directrix 2p F p V p 2p

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

Given the equation a) Write the equation in standard form

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

Given the equation a) Write the equation in standard form

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

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

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

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

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)

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

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

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

Now graph it………

V1 V2 F1 F2 C 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(2, -2) a = 5 c = 2 C F V

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

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