SOLUTION: Write an equation of a parabola that opens to the right, has a vertex at the origin, and a focus at (7, 0).

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write an equation of a parabola that opens to the right, has a vertex at the origin, and a focus at (7, 0).      Log On


   

Question 1119191: Write an equation of a parabola that opens to the right, has a vertex at the origin, and a focus at (7, 0).
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The vertex form of the equation of a parabola that opens to the right with vertex (h,k) is

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

In that formula, p is the directed distance from the vertex to the focus; since in this problem the parabola opens to the right, p is positive.

Then, since the vertex is (0,0) and the directed distance p from the vertex to the focus is 7, the equation is

%28x-0%29%5E2+=+%281%2F4%287%29%29%28y-0%29%5E2

or

x+=+%281%2F28%29%28y%5E2%29