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?

Question 117154: 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?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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

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