Question

Determine the center and radius of the following circle equation: x^2+y^2+20x+8y+35=0

Answer 1

center: (-10,-4)

radius: 9

Explanation:

Let's start off by moving the 35 to the other side and grouping the x and y terms we have

(x²+20x)+(y²+8y)= -35

Next we take the term with the x coeficcent, divide it by 2, and square it

so

for the x we would do (20/2)²=100

and make sure we add that to the 35

(x²+20x+100)+(y²+8y+16)= -35+100+16

next factor everythign to get

(x+10)²+(y+4)²=81

therefore the center is (-10,-4)

and the radius is √81 or 9