5. Find the inverse:

6. Find the inverse: ! = !" ! − ! + !

Review Sheet #2- Conics

Match each equation to the corresponding conic section:

______ ______ ______ ______

Write the equation of a parabola with the given characteristics:

1. Opens down, vertex at (3,4) with focal length of 5 units

2. Opens left, vertex at (2,-2) with focal length !! unit

Identify the center and radius of the circle:

3. a) b)

For each hyperbola, tell whether it’s vertical or horizontal, identify the center, and the coordinates of the 2 vertices.

4. a) b)

Parabola Reference:

|a| = 14c

c= Distance from vertex to focus

4c= Focal Width/Length (Width of parabola at focus)

Write the equation for the ellipse in standard form: 5. 6.

Name the conic & its orientation (horizontal/vertical). Then, find the vertex, foci, and equation in standard form. Then, sketch a graph.

7.

Sketch:

8.

9.

Write in vertex form, then find the vertex, directrix, and focal length.

10. 11.

Conic Word Problems

12.

13. A painter used a can of spray paint to make an image. The boundary of the image is described by the equation !!! − !"!+ !! − !!+ !" = !. Put this equation into standard form and describe whether curve is a circle, ellipse, parabola, or hyperbola. 14. The pool on an architectural floor plan is given by the equation !! + !!+ !! + !! = !. What point on the edge of the pol is farthest form the origin?

15. The walls of an elliptical room are given by the equation !!

!" +!!!" = !. Two people want to stand at

the foci of the ellipse so they can whisper to hear each other without anybody else hearing ( like in Grand Central Station!). What are the coordinates of the foci? 16. Astronomers discover a new comet. They study the path and discover that it can be modeled by a branch of a hyperbola with equation !!! − !"!− !"!! = !. a) Rewrite this equation in standard form and find the center of the hyperbola. b) Astronomers also discover a pair of twin planets at the foci of the comet. Where are the planets located?