Question

A parabola has a vertex at (2, 5) and a directrix at x = 8. Find the equation for this parabola. Explain how you got your answer.

Answer 1

parabola is a set of ponts that have same distance from the focus and directrix

Answer 2

how do you solve this question though

Answer 3

first find the focus, by using standart form of the equation of parabola:
\[(y-k)^{2}=4a(x-h)\]
(h,k) is the vertex and (a+h,k) is the focus

Answer 4

notice that vertex is halfway between directrix and focus