AATS
Section 10.2 Day 1 Notes: Conic Sections – Parabolas
Intersecting a plane with a double cone, we get curves known as CONIC SECTIONS. Depending on how
the plane and double cone intersect, we can get a CIRCLE, PARABOLA, ELLIPSE, or HYPERBOLA.
All of the conic sections are plane figures and can be represented in a coordinate plane.
Throughout this chapter we will be learning about each of the four conic sections. Today we will start
with PARABOLAS.
Definition: A parabola is the set of all points in a plane that are the same distance from a fixed line (the
directrix) and a fixed point not on the line (the focus).
Important Parts of a Parabola:
Standard Equation of a Parabola:
Opens Up/Down
2
 x  h   4c  y  k 
Opens Left/Right
2
 y  k   4c  x  h 
c  0 opens up
c  0 opens down
c  0 opens right
c  0 opens left
Vertex is  h, k 
“c” is the distance from the vertex to the focus/directrix
Identify the vertex, the focus, and the directrix of the parabola with the given equation. Then sketch a
graph of the parabola.
 x  2
 8  y  3
1) y 2  12 x
2)
Vertex: _______________
Vertex: _______________
Focus: ________________
Focus: ________________
Directrix: _______________
Directrix: _______________
3)
 x  3
2
 20 y
2
4) y 2  6  x  1
Vertex: _______________
Vertex: _______________
Focus: ________________
Focus: ________________
Directrix: _______________
Directrix: _______________