SOLUTION: What is the equation of the parabola with vertex (2 4) and focus (5 4)? A) {{{y=(1/3) (x-4)^2+2}}} B) {{{y=(1/12) (x-4)^2+2}}} C) {{{x=(1/3) (y-4)^2+2}}} D) {{{x=(1/12)

Question 1117777: What is the equation of the parabola with vertex (2 4) and focus (5 4)?
A)
B)
C)
D)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The focus is to the right of the vertex, so the parabola opens to the right; x is the dependent variable. So the answer is either C or D.

(Note also that choices A and B not only define parabolas that open upward instead of to the right; but they also define parabolas with vertex (2,4) instead of (4,2).)

The general equation of a parabola like that is

where (h,k) is the vertex and p is the directed distance from the vertex to the focus.

In your example, the directed distance from the vertex to the focus, p, is 3, so 1/4p is 1/12 -- so answer D.
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