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

Jul 19, 2017

The equation of parabola is ${y}^{2} = 20 x$

#### Explanation:

Focus is at$\left(5 , 0\right)$ and vertex is at $\left(0 , 0\right)$.

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

the equation of parabola is ${y}^{2} = 4 a x$ , $a = 5$ is the focal distance (the distance from vertex to focus).

Hence the equation of parabola is ${y}^{2} = 4 \cdot 5 \cdot x \mathmr{and} {y}^{2} = 20 x$

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