Intersections of planes and cones resulted in 4 separate conic sections.
Conic Section (conics): Parabolas, circles, ellipses, and hyperbolas, which are
formed when a plane intersects a double-napped cone.
1. Graph 𝑥 + 5
2
+ 𝑦−1
2
=4
2. Graph
𝑥+2 2
9
−
𝑦−1 2
16
=1
3. Write an equation of a parabola whose vertex is at (4, -2) and whose focus is at ( 4,1).
4. Write an equation of an ellipse with foci ( 3, 5) and ( 3, -1) and co-vertices at ( 1, 2) and ( 5, 2).
5. Identify the line(s) of symmetry for each conic section in each graph below.
Classify each conic. Then graph each equation.
6. 𝑥 − 3 =
1
2
𝑦−2
2
7. 4𝑥 2 + 𝑦 2 − 8𝑥 − 8 = 0
8. You are walking into a tunnel whose opening can be modeled by the equation
9𝑥 2 + 16𝑦 2 − 18𝑥 + 64𝑦 − 71 = 0. Write an equation for the curve of the opening in
standard form. What is the shape of the tunnel opening? Graph the equation.