Question

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

Answer 1

The radius is 4

Step-by-step 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