Answer:

Step-by-step explanation:
So we want to find the equation of a circle with the center at (4,5) and which passes through the point (-3,5).
First, recall the standard form for a circle, given by the equation:

Where (h,k) is the center and r is the radius.
We already know that the center is (4,5). So, substitute 4 for h and 5 for k. Therefore, our equation is now:

Now, we need to find the radius.
Remember that our circle passes through the point (-3,5). In other words, when x is -3, y is 5. So, substitute -3 for x and 5 for y to solve for r. Therefore:

Subtract within the parentheses:

Square:

Square root:

Therefore, the radius is 7.
So, substitute 7 into our equation, we will acquire:

Square:

So, our equation is:

And we're done!