Question

Determine the center and radius of the following circle equation: x^2+y^2-8x+6y-75=0 x 2 +y 2 −8x+6y−75=0 Center: \big(( , \big)) Radius:

Answer 1

Compare x^2 +y^2-8x-6y=75 with the general circle equation x^2+y^2 -2ax-2by+c=0

-2a =-8 And -2b=-6

a=4 b=3

c=-75

To find the radius use the equation

r^2=a^2+b^2-c

r^2=4^2+ 3^2-(-75)

r^2=25+75=100

r=10(radius is always positive)

Hence the center is (4,3) and radius 10

Explanation: