SOLUTION: Which of the following is an equation of the circle that has its center at C(2,3) and passes through A(5,7) in the standard (x,y)coordinate plane?

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The general equation for a circle is where (h,k) is the center and r is the radius. Since we know the center is (2,3), we know that the equation looks like




Now we only need the radius. Since the point A(5,7) is on the circle, we need to find the distance from A to the center to find the radius
Start with the given distance formula
where is the first point and is the second point

Plug in , , ,

Evaluate to get -3. Evaluate to get -4.

Square each value

Add

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

So the distance between (2,3) and (5,7) is 5 units. This means the radius is 5 units.

So which means


So the equation of the circle is