What is the focus of the parabola x + 5(y - 3)^2 = 6x+5(y3)2=6?

1 Answer
Oct 23, 2016

(119/20, 3)(11920,3)

Explanation:

Write in vertex form for a left or right opening parabola, x = a(y - k)^2 + hx=a(yk)2+h:

#x = -5(y - 3)^2 + 6

The directed focal length, f, for all parabolas is:

f = 1/(4a)f=14a

Substitute -5 for a:

f = 1/(4(-5))f=14(5)

f = -1/20f=120

The general form for the focus of a left or right opening parabola is:

(h + f, k)(h+f,k)

Substitute 6 for h, 3 for k, and -1/20120 for f:

(6 + -1/20, 3)(6+120,3)

(119/20, 3)(11920,3)