Review for Parabolas.

1. Find the equation of the parabola with vertex ( 3,5 ) and focus at ( 3, -2).
2. Find the equation of the parabola with focus at ( -5, 0) and directrix x = 5.
3. Find the equation of the parabola with vertex at ( 3, 1) and passes through ( 4, 3) and ( 2, 3).
4. Find the vertex, focus and directrix of parabola.

a) ( x + 2)² = -8 ( y + 2) b) y² - 2y - 8x + 1 = 0

5. Graph each parabola. Include vertex and focus.

a) x² + 6x – 4y + 1 = 0 b) ( y + 4)² = 12 ( x + 2)

Review for Ellipses

1) Find the equation of the ellipse with vertex at ( 6, 4) and foci at ( -4, 4) and ( 4, 4).

2) Find the equation of the ellipse with foci at (0, 0) and ( 4, 0) and major axis has a length of 8.

3) Find the equation of the ellipse with center at ( 3,4) and passes through ( 8, 4) and ( -2, 4) and the minor axis has a length of 4.

4) Find the center, vertices and foci and graph each ellipse.

a) b) 4x² + 9y² - 16x -18y = 11

Review for Hyperbolas

1) Find the center, vertices and foci. A) 9( y + 2)² - 4(x -1)² = 36 B) x² - y² - 4x – 6y = 6

2) Find the equation of the hyperbola that has a center of ( -1, 3), vertex ( 1, 3) and focus of ( 2,3).

3) Find the equation of the hyperbola that has center at ( 1, 4), focus ( 7, 4) and vertex ( 3,4) .

4) Find the equation of the asymptotes for ( don’t worry about this one)

5) Find the equation of the hyperbola with center (5, 3) , vertex ( 5, 6) and passes through ( 1, 8).

6) Graph each hyperbola. Include the fundamental rectangle, asymptotes, and the hyperbolic curves.

a) y² - 4x² + 6y + 32x = 59 b) 4x² - y² + 32x + 6y + 39 = 0