Parabolas

1
Section 10.2

• Parabolas

2
PARABOLA with vertex at (0,0)
y2 4px
Opens left or right
x2 4py
Opens up or down
3
PARABOLA
(y k) 2 4p (x h)
Opens left or right
(x h) 2 4p (y k)
Opens up or down
4
PARABOLA
(y k) 2 4p (x h)
Opens left or right
Focus (h p, k)
Directrix x h - p
5
PARABOLA
(x h) 2 4p (y k)
Opens up or down
Focus (h, k p)
Directrix y k - p
6
Write an equation of the parabola whose vertex is
at (2, 1) and whose focus is at (3, 1).
SOLUTION
Find h and k The vertex is at (2, 1), so h
2 and k 1.
(y 1) 2 4p(x 2).
7
Write an equation of the parabola whose vertex is
at (2, 1) and whose focus is at (3, 1).
SOLUTION
(2, 1)
Find p The distance between the vertex (2, 1),
and the focus (3, 1) is p.
(h p, k) (-3, 1) (-2 p, 1) (-3, 1)

-2 p -3
so p 1 or p 1. Since p lt 0, p 1.
The standard form of the equation is (y 1) 2
4(x 2).