Question

What is the equation of a parabola whose vertex is (0, 5) and whose directrix is
x = 2?

Answer 1

you know what this looks like?

Answer 2

no not really

Answer 3

draw the vertical line \(x=2\) and then put a point at \((0,5)\)

Answer 4

ok good

Answer 5

now the vertex is half way between the focus \((0,5)\) and the line \(x=2\) so it is at \((1,5)\)

Answer 6

and the picture shows you that the parabola opens to the left, not the right, because all points are equidistant from the focus and directrix

Answer 7

so it's negative

Answer 8

general form in this case will look like
\[(y-k)^2=4p(x-h)\] where the vertex is \((h,k)\) and \(p\) is the the distance between the focus and the directrix

Answer 9

yeah it is negative, meaning \(4p\) is negative
in fact in this case since the distance between the focus and the vertex is 1 , it is
\[(y-5)^2=-4x\]

Answer 10

oh i said something wrong
\(p\) is the distance between the focus and the vertex, not the distance between the focus and the directrix
sorry
answer is right though

Answer 11

so do i distribute it?

Answer 12

so because of the two
it would be
\[(y-5)^{2}-8x\]

Answer 13

\[(y-5)^{2}=-8x\]