Question

Find the equation of the parabola with focus (2, 3) and directrix y = -1.
es

Answer 1

Y=1/8^2-1/2x + 3/2 would be the answer

Answer 2

Below in bold.

Explanation:

Let (x, y) be a point on the parabola. As the graph is a parabola, the distance of this point to the focus is equal to the distance of this point from the directrix. So:

√(( x - 2)^2 + (y - 3)^2) = y - (-1)

Squaring both sides:

(x - 2)^2 + (y - 3)^2 = (y + 1)^2

x^2 - 4x + 4 + y^2 - 6y + 9 = y^2 + 2y + 1

x^2 - 4x + 4 + 9 - 1 = 2y + 6y

8y = x^2 - 4x + 12

y = 1/8(x^2 - 4x + 12)

or we can write it as

y = 1/8x^2 - 1/2 x + 3/2.