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?

Algebra ->  Pythagorean-theorem -> 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?       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The general equation for a circle is %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 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

%28x-2%29%5E2%2B%28y-3%29%5E2=r%5E2


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
d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 where is the first point and is the second point

d=sqrt%28%282-5%29%5E2%2B%283-7%29%5E2%29 Plug in x%5B1%5D=2, x%5B2%5D=5, y%5B1%5D=3, y%5B2%5D=7

d=sqrt%28%28-3%29%5E2%2B%28-4%29%5E2%29 Evaluate 2-5 to get -3. Evaluate 3-7 to get -4.

d=sqrt%289%2B16%29 Square each value

d=sqrt%2825%29 Add

d=5 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 r=5 which means r%5E2=5%5E2=25


So the equation of the circle is %28x-2%29%5E2%2B%28y-3%29%5E2=25