Question

What is the radius of a circle whose equation is X^2 plus Y^2 -10X +6 X +18=0?

Answer 1

ANSWER

The radius is 4

EXPLANATION

The given equation is:

${x}^{2} + {y}^{2} - 10y + 6x + 18 = 0$

We complete the square to get the expression in standard form:

${x}^{2} + 6x + {y}^{2} - 10y + 18 = 0$

${x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25$

We factor using perfect squares to get:

${(x + 3)}^{2} + {(y - 5)}^{2} = 16$

This implies that,

${(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2}$

Comparing to

${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$

The radius is r=4