Given:
The vertex is (-2,5).
[tex](h,k)=(-2,5)[/tex]And the focus is (-2,6).
Required:
To find the equation of the parabola.
Explanation:
The equation of a parabola in vertex form is
[tex]y=a(x-h)^2+k[/tex]Here,
[tex](h,k)=(-2,5)[/tex]Therefore,
[tex]\begin{gathered} y=a(x-(-2))^2+5 \\ \\ y=a(x+2)^2+5 \end{gathered}[/tex]And given that focus is
[tex](h,k+\frac{1}{4}a)=(-2,6)[/tex][tex]\begin{gathered} k+\frac{1}{4}a=6 \\ \\ 5+\frac{1}{4}a=6 \\ \\ \frac{1}{4}a=6-5 \\ \\ \frac{1}{4}a=1 \\ \\ a=4 \end{gathered}[/tex]Therefore, the equation of parabola is,
[tex]y=4(x+2)^2+5[/tex]Final Answer:
The equation of parabola is,
[tex]y=4(x+2)^{2}+5[/tex]