Answer:
\(x=\frac{1}{12}(y-4)^{2}-5\)
Step-by-step explanation:
In this problem we have that
The vertex and the focus has the same y-coordinate, therefore, is a horizontal parabola
The equation of a horizontal parabola is of the form
\(x=a(y-k)^{2}+h\)
where
(h,k) is the vertex
The coordinates of the focus are equal to \((h+\frac{1}{4a} ,k)\)
we have in this problem
\(focus (-2,4)\)
\(vertex (-5,4)\)
substitute
\((h,k)=(-5,4)\)
\((-2,4)=(-5+\frac{1}{4a} ,4)\)
so
Find the value of a
\(-2=-5+\frac{1}{4a}\\ \\\frac{1}{4a}=3\\ \\a=\frac{1}{12}\)
The equation of the horizontal parabola is equal to
\(x=\frac{1}{12}(y-4)^{2}-5\) ------> open to the right
