Question

Write the equation of the parabola with focus (1, -2) and vertex (1, -5)

Answer 1

y=x^2/12 - x/6 - 59/12

Answer 2

i got it wrong the first time

Answer 3

the focus and vertex have the same x-coordinate which suggest that this is a parabola opening upwards (the vertex is below the focus). so the equation has the form:

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

where (h, k) is your vertex, and p represents the distance from your vertex to the focus. in your case p=3, h=1, k=-5. so your equation is:

(x - 1)^2 = 4*3*(y + 5) or (x - 1)^2 = 12(y + 5)