Answer:
[tex](y-5)^2=12(x+2)[/tex]
Step-by-step explanation:
Since the focus point is directly right of the vertex, the axis of symmetry will be horizontal, which means that we use the equation [tex](y-k)^2=4p(x-h)[/tex] where [tex](h,k)[/tex] is the vertex and [tex](h+p,k)[/tex] is the focus point.
Since we know our vertex to be [tex](h,k)\rightarrow(-2,5)[/tex] and our focus point to be [tex](h+p,k)\rightarrow(1,5)[/tex], the distance from the vertex to the focus point is [tex]p=3[/tex].
Hence, the equation is:
[tex](y-5)^2=4(3)(x-(-2))\\\\(y-5)^2=12(x+2)[/tex]
