Question

Find the standard form of the equation of the parabola with a focus at (5, 0) and a directrix at x = -5. (5 points) y = 1 divided by 20 x2 20y = x2 x = 1 divided by 20 y2 y2 = 20x

Answer 1

ANSWER

$y = \frac{1}{20} {x}^{2}$

EXPLANATION

We want to find the equation of the parabola with a focus at (5, 0)

and a directrix at x = -5.

The distance from the focus to the vertex is the same as the distance from the vertex to the directrix.

This implies that the parabola has its vertex at the origin. This distance is

$p = 5$

This parabola has equation of the form

${x}^{2} = 4py$

We plug in p= 5 to get

${x}^{2} = 4 \times 5y$

${x}^{2} = 20y$

Or

$y = \frac{1}{20} {x}^{2}$