Question

Write the equation of a parabola with a vertex at (5, 2) and a directrix y = 1.

Answer 1

Answer:

${(x - 5)}^{2} = 4(y - 2)$

Step-by-step explanation:

A parabola with vertex at (5, 2) and a directrix y = 1 is a vertical parabola that opens up.

The distance from the vertex to the directrix p=2-1=1 units.

The equation is given by:

${(x - h)}^{2} = 4p(y - k)$

where (h,k)=(5,2) is the vertex.

We substitute the values to get:

${(x - 5)}^{2} = 4(1)(y - 2)$

${(x - 5)}^{2} = 4(y - 2)$

Or

$y = \frac{1}{4} ( {x - 5)}^{2} + 2$