Practice!

Sample Problem

Find the focus of the parabola with the equation –y2-3x-20y-92=0

Solution

To find the focus, convert this equation to standard form by completing the square:

–y2-3x-20y-92=0

-3x-92=y2+20y

-3x-92+100=y2+20y+100

-3x+8=(y+10)2

-3(x-8/3)=(y+10)2

Comparing -3(x-8/3)=(y+10)2 to

(y-k)2=4p(x-h)

k=-10

p=-3/4

h=8/3

The focus of the parabola is therefore (h+p, k) – [(8/3)-(3/4), -10]=(23/12, -10)