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?