Question

Find an equation of the parabola with vertex (-1, -5) and directrix x=-7.

Answer 1

Answer:

Base on the vertex (h, k) and the distance p between vertex and directrix, the standard form of parabola is written as:

(x – h)^2 = 4*p(y – k)

We have (-1, -5) as vertex.

=> (x + 1)^2 = 4*p(y + 5)

Now, we find p:

The distance between (-1, -5) and x = -7 is calculated by:

|-1 -(-7)| = |6| = 6

=> (x + 1)^2 = 4*6(y + 5)

=> (x + 1)^2 = 24(y + 5)

Hope this helps!

:)

Answer 2

Answer:

(y + 5)² = 24(x + 1)

Step-by-step explanation:

(x - h)² = 4p(y - k)

(h,k) = (-1,-5)

p = -1 - (-7) = 6

4p = 4(6) = 24

Equation

(y - -5)² = 24(x - -1)

(y + 5)² = 24(x + 1)