1. Parabola (Left\Right) Hyperbola (Left Right)
Parabola Parts
Equation of Ellipse (1)
Parabola (Up\Down)
Equation of Ellipse (2)
Parabola (Left\Right)
Hyperbola (Left Right)
Equation of Parabola (Vertex, Focus)
Hyperbola (Up Down)
Equation of Parabola (Vert, Direct)
Equation of Hyperbola (1)
Equation (Line tangent to circle at
a point)
Equation of Hyperbola (2)
Ellipse (Tall)
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Problems may be more difficult on test. Consult homework assignment. Not all topics covered.
Ellipse (Wide)

2. Up\down parabola Right (pos)\Left(neg) parabola
Vertex
Focus
Directrix
Axis of Symmetry
How to graph
1) Opens
2) Vertex, aos
3) Find p
4) Focus
5) Directrix
6) Latus Rectum = |4p| through focus
Focus – On a.o.s., is inside the parabola
Directrix – perpendicular to a.o.s, is outside the parabola
All points on the parabola are equidistant from the focus and the directrix

3. Don’t have to necessarily memorize, just think about these.
How to graph
1) Opens
2) Vertex\aos
3) Find p
4) Focus
5) Directrix
Down
(3, 4); x = 3
p = -2
(3, 4 + (-2)) = (3, 2)
x = 3
y = 4 – (-2)  y = 6
y = 6
(3, 4)
Latus Rectum
|4p| = 8
(3, 2)
Don’t have to necessarily memorize, just think about these.

4. Don’t have to necessarily memorize, just think about these.
1) Opens
2) Vertex, aos
3) Find p
4) Focus
5) Directrix
Right
(-5,-2), y = -2
(-5,-2)
Latus Rectum
y = -2
|4p| = 1\2
Don’t have to necessarily memorize, just think about these.

5. Equation of parabola given vertex and focus.
Vertex (2,1) Focus (4,1)
1) Opening
2) Vertex
3) Find p
4) Plug in parts

6. Equation of parabola given vertex and directrix.
Vertex (2,-3) Directrix y =
1) Opening
2) Vertex
3) Find p
4) Plug in parts

7. Equation of tangent line given center, point
Find center
Other point
2) Find slope
3) Perp Slope
4) Eq of line
(3, -1)
(x - 3)2 + (y + 1)2 = 20
(5, 3)
(5,3) is point on circle

8. 1) Tall or Wide? 2) Find center Find a and plot Find b and plot
Find c and plot

9. 1) Tall or Wide? 2) Find center Find a and plot Find b and plot
Find c and plot

10. NOTE: If you have a and b, you don’t need c
Vertices: (4,0), (-2,0) Foci: (2,0), (0,0)
1 – Find Center
2 – Tall or Wide
3 – Find a: b: c:
4 – Find what you don’t have
5 – Plug it in

11. NOTE: If you have a and b, you don’t need c
Co-Vertices: (5,-1), (-3,-1) Foci: (1,8), (1,-10)
1 – Find Center
2 – Tall or Wide
3 – Find a: b: c:
4 – Find what you don’t have
5 – Plug it in

12. Steps
1 – Find Center
2 – Find a and plot
3 – Find b and plot
4 – Make box and sketch asymptotes
5 – Find c, foci
6 – Sketch
7 – Equation of asymptotes

13. Steps
1 – Find Center
2 – Find a and plot
3 – Find b and plot
4 – Make box and sketch asymptotes
5 – Find c, foci
6 – Sketch
7 – Equation of asymptotes

14. Vertices: (4,0), (-2,0) Foci: (5,0), (-3,0)
1 – Find Center
2 – Up\Down, or Left\Right
3 – Find a: b: c:
4 – Find what you don’t have
5 – Plug it in

15. Vertices: (1,-3), (1,5) Foci: (1,-5), (1,7)
1 – Find Center
2 – Up\Down, or Left\Right
3 – Find a: b: c:
4 – Find what you don’t have
5 – Plug it in