Warm UpRewrite each equation in information form. Then, graph and find the coordinates of all focal points.

1) 9x2 + 4y2 + 36x - 8y + 4 = 0

2) y2 - 4x2 - 8x - 18y + 13 = 0

3) Write an equation of the parabola described.a) Directrix: y = -2 and vertex (1, 3)

b) Focus (-4, 5) , Directrix: x = 0

Homework Questions?

Trashketball

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1) Convert the point (-5, -12) to polar form. (remember no negative angles)

2) Convert the point (5, 5.5r) to rectangular form.

1) Complete the three polar points so that they will have the same graphic representation as (-3, 100), but different numerical values for the

angle.A. (-3, ________)B. (3, +_______)C. (3, -_______)

2) Convert the rectangular equation to polar form (solve for r).

x2 + y2 -2x + 3y = 0

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1) Convert to rectangular:

a) ( 2, 240)

b) (-3,3π/4)

c) (1, -210)

2) Convert the polar equation to rectangular.

r = 5cosθ

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1) Determine the polar coordinates of (-4, 4) (Remember: no negative angles)

2) Complete the ordered pairs for points on the graph of r = 3 + 3cosθ

a) ( ____, 0º) b) ( _____, 60º) c) (_____, 180º)

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Given r = mcos(nθ) explain the effect of m and n on the graph

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1) y = -¼(x – 3)2 + 1

2) x = 4y2 + 16y + 19

What is the vertex, focus and directrix of the parabola with equation given…

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1) What are the foci of the ellipse with equation x2 + 4y2 = 36?

2) What type of conic is the graph of x2 + 25y2 = 50? State the center.

3) What type of conic is the graph of x2 – y2 – 2x – 4y = 28?

State the center.

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Give the special name and graph each of the following…

1) r = 4cos(3θ)2) r = 1 + 3sinθ3) r = -3sinθ

Find the foci, length of the transverse and conjugate axes, and equations of the asymptotes of the hyperbola with equation

2 2( 4) ( 6)1

25 9

y x

Write an equation of the conic section described.

1) parabola with focus (-2, 4) and directrix y = 0.

2) Ellipse with endpoints of the major axis (-2, 5) and (-2, -1) and foci (-2, 4) and (-2, 0)

For the ellipse: 4(x + 4)2 + 9(y – 1)2 = 36, graph and determine the length of the major and minor axes. Also determine the coordinates of the foci.

For the hyperbola: 4x2 – y2 + 8x – 6y = 9, graph, determine the length of transverse and conjugate axes, foci and equation of the asymptotes.