Question

The focus of the parabola is (-1, -9/4), and the directrix is the line y = -7/4. Show that the point (-2,-3) on the parabola is the same distance from the focus as from the directrix.

Answer 1

Well, I do not know what the parabola has to do with this.
We are asked the distance from
(-2,3) to (-1, -9/4)
and from that same point
(-2,3) to the horizontal line y = -7/4

The second part is trivial
-7/4 to 3 is 12/4 + 7/4 = 19/4

we will actually have to do the first distance and hope it comes out 19/4

(-2,3) to (-1, -9/4)

d^2 = (-9/4 - 12/4)^2 + 1^2
d^2 = (-21/4)^2 + (4/4)^2
d^2 = (1/4^2) (441+16) = (1/4^2)(457)
d = (1/4) sqrt 457
hmmm, something is wrong
sqrt 457 is not 19