EXPLANATION:
Given;
We are given the equation of a parabola as shown below;
[tex]y^2-4y=-4x-8[/tex]
Required;
We are required to find the focus of the parabola.
Step-by-step solution;
We re-write this equation and express x in terms of y;
[tex]\begin{gathered} y^2-4y=-4x-8 \\ y^2-4y+8=-4x \\ Multiply\text{ all through by }-1: \end{gathered}[/tex][tex]\begin{gathered} -y^2+4y-8=4x \\ Divide\text{ all through by 4:} \end{gathered}[/tex][tex]\frac{4x}{4}=\frac{1}{4}(-y^2+4y-8)[/tex][tex]x=-\frac{1}{4}(y^2-4y+8)[/tex]
We now write this out in the vertex form which is;
[tex]\begin{gathered} x=a(y-b)^2+c \\ Where:vertex=(b,c) \end{gathered}[/tex]
We now simplify the right side of the equation;
[tex]x=-\frac{1}{4}((y-2)^2-4+8)[/tex][tex]undefined[/tex]
