Answer:
[tex](y + 3)^2=14(x + \frac{3}{2} )[/tex]
Step-by-step explanation:
We want to find the equation of the parabola in the focus at (2, -3), the directrix x+5=0.
We know that the vertex is the midpoint of the focus and the directrix(where it intersect the axis of symmetry)
The midpoint of x=-5 and x=2 is x=-1.5
The y-coordinate of the vertex is still -3.
So the vertex is (-1.5,-3)
This is a horizontal parabola that opens to the right.
The equation is of the form
[tex](y-k)^2=4p(x-h)[/tex]
The vertex is (h,k)=(-1.5,-3) and p=|2--1.5|=3.5
We substitute to get:
[tex](y- - 3)^2=4 \times 3.5(x- - \frac{3}{2} )[/tex]
[tex](y + 3)^2=14(x + \frac{3}{2} )[/tex]
