Answer
$(y-5)^2=20(x-5)$
Work Step by Step
Step 1. Identify the given quantities: parabola vertex $V(5,5)$, directrix is the y-axis.
Step 2. With the above information, we can write a general equation as $(y-k)^2=4p(x-h)$
Step 3. The vertex is at $(h,k)$, thus $h=5, k=5$
Step 4. The directrix is $x=h-p$ and for y-axis $x=0$ we have $5-p=0$ thus $p=5$
Step 5. The equation for the parabola is $(y-5)^2=20(x-5)$
