Find the equation for the circle with center (4,5) and passing through (-3,5).

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!

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step-by-step explanation: