The given information is:
- The vertex of the parabola is (6,2)
- The equation of its directrix is y=0
As the directrix is y=0, this means we have a vertical parabola.
The standard form of the equation of a vertical parabola is given by:
[tex](x-h)^2=4p(y-k)[/tex]
Where (h,k) is the vertex of the parabola, and p is given by the directrix equation:
[tex]y=k-p[/tex]
Let's start by finding p:
[tex]\begin{gathered} (h,k)=(6,2) \\ h=6,k=2 \\ y=k-p \\ 0=2-p \\ \therefore p=2 \end{gathered}[/tex]
Now, replace the known values and find the equation:
[tex]\begin{gathered} (x-6)^2=4*2*(y-2) \\ \therefore(x-6)^2=8(y-2) \end{gathered}[/tex]
The answer is above.
