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)

Algebra ->  Quadratic-relations-and-conic-sections -> 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)      Log On


   

Question 1117777: What is the equation of the parabola with vertex (2 4) and focus (5 4)?
A) y=%281%2F3%29+%28x-4%29%5E2%2B2
B) y=%281%2F12%29+%28x-4%29%5E2%2B2
C) x=%281%2F3%29+%28y-4%29%5E2%2B2
D) x=%281%2F12%29+%28y-4%29%5E2%2B2
Answer by greenestamps(13200) About Me  (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

x-h+=+%281%2F%284p%29%29%28y-k%29%5E2

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.