Question
Find the equation of the parabola w/ v(3,-4) and with directrix y=0.
Answers
Steve
Since the distance from the vertex to the directrix is 4, then the standard parabola
x^2 = 4py
has p=4. So, with the translation of the vertex to (3,-4), and the directrix above the vertex, the parabola opens downward, so the equation is
(x-3)^2 = -16(y+4)
confirmed at
http://www.wolframalpha.com/input/?i=parabola+(x-3)%5E2+%3D+-16(y%2B4)
You may, of course massage that equation into the form desired.
x^2 = 4py
has p=4. So, with the translation of the vertex to (3,-4), and the directrix above the vertex, the parabola opens downward, so the equation is
(x-3)^2 = -16(y+4)
confirmed at
http://www.wolframalpha.com/input/?i=parabola+(x-3)%5E2+%3D+-16(y%2B4)
You may, of course massage that equation into the form desired.