how do you write an equation given the focus (-2,3) and the directrix -2 and 1/12?

Question

please show me the step i have 2 do the rest by myself.

X= -2 and 1/12

Answer 1

EDIT: After seeing that the directrix was x = -25/12,
rather than y = -25/12 (if I understand -2 and 1/12
correctly), I had to edit my previous answer a bit.
Hopefully, this is now the correct version.

Choose any point on the parabola and call it (x, y).

The perpendicular line from (x, y) to the directrix, meets
the directrix at the point (-25/12, y)

The distance from (x, y) to (-2, 3) is the same as the
distance from (x, y) to (-25/12, y), from the definition
of a parabola.

Now you can use the distance equation between two
points for both these lines and set them equal to each other.

After simplification, you should end up with an equation
relating x to y.

EDIT 2:
It's been nearly a day now.
Did you get the same answer as me?
x = 6y^2 - 36y + 1247 / 24

Answer 2

you can write it directly using definition of parabola

(x+2)^2+(y-3)^2= (x+2.5)^2
which is
x^2+4x+4+y^2-6y+9= x^2+5x+6.25
so x= y^2-6y+6.75