Question

Write the equation for a parabola with a focus at (-2,5) and a directrix at x=3 Answer has to be in Y=____ Format

Answer 1

Answer:

Step-by-step explanation:

The vertex of a parabola is directly in between the focus and the directrix. That means that the vertex of this parabola is at (1/2, 5). A parabola wraps itself around the focus and away from the directrix, so this parabola opens to the left. One other thing that we need to know is the distance between the vertex and the focus, the p value in the equation. So here's the equation we need (it's not a y= equation, though):

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

So here's what we know from the info above:

p = 5/2

h = 1/2

k = 5

and filling in:

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

$-(y-5)^2=10(x-\frac{1}{2})$ and then solving for x:

$-\frac{1}{10}(y-5)^2+\frac{1}{2}=x$