Question

A parabola has a focus of (-1, 5 4 ) and a directrix of y = 3 4 . What is the parabola’s equation?

Answer 1

y = ax^2 + bx + c standard form of a parabola

Answer 2

really?

Answer 3

can you explain why?

Answer 4

this is what you know



well a standard form is

(x -h)^2 = 4a(y - k)

where (h, k) is the vertex and a is the focal length

the distance between the vertex and focus is called the focal length (a)

its the same distance from the vertex to the directrix.

so you know h = -1 since the line of symmetry is x = -1 from the vertex

so

2a = 54 - 34

the k value in the vertex is

54 - a =

then substitute h = -1, k = 54 - a and your value for a into the equation above and expand