Download Conics Review Sheet - Garnet Valley School District

Conics Review Sheet
Pre-Calc. for AP Prep.
Name: ___________
No Calculator
1. Find the coordinates of any points where the line x – y = 2 and the circle x 2  y 2  4 intersect. If
necessary, note that the graphs are tangent or that they do not intersect.
2. Find the equation of the circle having (2, 5) and (-2, -1) as endpoints of a diameter.
3. Find the coordinates of the vertices and the foci of the ellipse with the equation 9 x 2  5 y 2  45 .
Sketch the ellipse.
4. Find an equation for the ellipse that has (2, -4) and (2, 8) as its vertices and (5, 2) and (-1, 2) as
endpoints of the minor axis.
5. Find an equation for the hyperbola that has a center at (0, 0), a vertex at (0, -3) and a


focus at 0, 13 .
6. Find an equation of a hyperbola that has a vertex at (0, -3) and has asymptotes with equations
2
y   x  5.
3
7. Find the coordinates of the vertex and focus and the equation of the directrix for the parabola
x3 
1
 y  22 .
8
8. Sketch each of the following. Give the coordinates of the center, and for graphs other that circles, any
foci, any vertices, and any asymptotes.
a. 4 x 2  4 y 2  8x  24 y  15  0
b.
y 2  x2  2 y  4x  4  0
9. A parabolic headlight has its bulb located at its focus, one inch from the vertex. If the total depth of the
headlight is 2 inches, what is the diameter of the headlight?
10. Find the lengths of the minor and major axis of an ellipse that can be drawn using a string 8 feet long
and two tacks anchored 1 foot apart from each other.
Identify the conic section without completing the square.
11.
5x2 – 2xy + 5y2 – 12 = 0
12.
23x 2  26 3 xy  3 y 2  144  0
13.
4xy + 3y2 + 4x + 6y – 1 = 0
14.
10x2 + 24xy + 17y2 - 9 = 0
15.
Graph the curves over the given interval
16.
Graph the curves by eliminating
the parameter.
x = -sint
y = -cost
0 < t < 2π
x = 1 + 3 cost
y = -1 + 2sint
0<t<π
17.
Give two different sets of parametric equations for each rectangular equation.
y = 4x3 + 5
Calculator Section
Graph the following.
1.
x 2  2 3 xy  3 y 2  12 3 x  12 y  0
2.
34x2 – 24xy + 41y2 – 25 = 0
Graph the following conics:
3.
r
6
3  6sin 
4.
r
2
1  cos 