Find the center and radius of the following circle: x^2-4x+y^2+6y-36=0

Question

find center and radius of circle

Answer 1

The general form for a circle is:

 

     (x-h)² + (y-k)² = r²

 

where (h, k) is the location of the center and r is the radius.

 

     x²-4x+y²+6y-36=0

     x² - 4x + y² + 6y = 36

 

Complete the square on both the x terms and the y terms

 

     x² - 4x + 16 + y² + 6y + 36 = 36 + 16 + 36

     (x-4)² + (y+6)² = 88

 

Center at  (h, k) = (4, -6)

Radius = √88 = 2√22