Question

What is the equation of the parabola which has a vertex at the origin a focus at (5,0)?

Answer 1

The equation of parabola is `y^2=20x`

Explanation:

Focus is at`(5,0)` and vertex is at `(0,0)`.

The focus is at right of vertex , so parabola opens right, for which

the equation of parabola is `y^2=4ax` , `a =5` is the focal distance (the distance from vertex to focus).

Hence the equation of parabola is `y^2=4*5*x or y^2=20x`

graph{y^2=20x [-80, 80, -40, 40]}