(x - 2)^2 = -3 (y - 1) ... find the vertex, focus and directrix of this parabola.?

Question

PLEASE HELP ME!!

Answer 1

The vertex is easy to see in that form.

One common form of a parabola is:

(x - h)² = 4p(y - k)

Your equation is in that form.

The vertex is (h, k), or (2, 1).

The focus and directrix are p units "inside" and "outside" the parabola.

4p = -3
p = -3/4

Since the parabola opens "downwards" (because x is the thing that is squared, and p is negative), the focus is:

(2, 1 - 3/4) = (2, 1/4)

And the directrix is the horizontal line p units above the vertex.

y = 1 + 3/4 = 7/4