How do you find the center and radius of the circle X^2-8x+16+y^2+10y+25=81?

1 Answer
Jan 22, 2017

The given equation can be converted to the form (x - h)^2 + (y - k)^2 = r^2 by observing the perfect squares within the equation. (h,k) is the center and r is the radius.

Explanation:

Given: x^2 - 8x + 16 + y^2 + 10y + 25 = 81" [1]"

Please observe that: x^2 - 8x + 16 = (x - 4)^2 this makes equation [1] become:

(x - 4)^2 + y^2 + 10y + 25 = 81" [2]"

The y terms are, also, a perfect square: y^2 + 10y + 25 = (y - -5)^2

(x - 4)^2 + (y - -5)^2 = 81" [3]"

Finally, the constant term, 81 = 9^2:

(x - 4)^2 + (y - -5)^2 = 9^2

The center is the point (4,-5) and the radius is 9.