circle C,centre at the point A (5,0) has equation of x^2+y^2-10x+9=0. find radius of C

Question

i already worked out the coordinate A but i dont know how to find the radius.

 

Answer 1

Given equation x^2+y^2-10x+9 = 0

x^2-10x+y^2+9 = 0

Add 25 to each side to complete square.

x^2-10x+25+y^2+9 = 25

Subtract 9 from each side.

x^2-10x+25+y^2+9-9 = 25-9

(x-5)^2+(y-0)^2 = 16

(x-5)^2+(y-0)^2 = 4^2

Compare it to standard form of circle (x-h)^2+(y-k)^2 = r^2

Center is (5,0) and radius is 4.

Radius of C is 4.