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Question

Determine the center and radius of his circle:

x^2+20x +y^2-10y+ 100=0

Answer 1

Use completion of the square from Algebra 1.

x² + 20x + y² - 10y = -100

x² + 20x + 10² + y² - 10y + 5² = -100 + 10² + 5²

(x + 10)² + (y - 5)² = 5²

Answer 2

The standard form of equation of a circle is:

(x-h)² + (y-k)² = r²

where (h,k) is the center of the circle, and

r is the radius.

x²+20x +y²-10y+ 100=0

x²+20x +y²-10y = -100

Do the completing of squares:

x²+20x+ __ +y²-10y+__ = -100+__+__

If x²+bx+ c is a perfect square trinomial, then c = (b/2)².

(20/2)² = 100

(-10/2)² = 25

x²+20x+ 100 +y²- 10y + 25 = -100+ 100 + 25

(x+10)² + (y-5)² = 25

Center = (-10,5)

radius (r) = 5