Question

Which is the equation of a parabola with focus (-2, -4) and vertex (-4, -4)?

Answer 1

Answer:

C.

Step-by-step explanation:

If we plot the vertex and the focus, since the parabola wraps itself around the focus, we can see that this is parabola that opens up to the right.  The distance between the vertex and the focus is 2 units.  The equation for this type of parabola is:

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

where h and k are the coordinates of the vertex and p is the distance between the vertex and the focus.  We already know all of that info so we can jump right to filling in the equation:

$4(2)(x+4)=(y+4)^2$ which of course simplifies to your answer:

$8(x+4)=(y+4)^2$