Question

The equation of a circle is x2+y2−12x+6y+20=0 .

What is the radius of the circle?

r = ?

Answer 1

The radius is r=5 units

Explanation:

we know that

The equation of the circle in standard form is equal to

`(x-h)^(2)+(y-k)^(2)=r^(2)`

where

(h,k) is the center and r is the radius

we have

`x^(2)+y^(2)-12x+6y+20=0`

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`(x^(2)-12x)+(y^(2)+6y)=-20`

Complete the square twice. Remember to balance the equation by adding the same constants to each side

`(x^(2)-12x+36)+(y^(2)+6y+9)=-20+36+9`

`(x^(2)-12x+36)+(y^(2)+6y+9)=25`

Rewrite as perfect squares

`(x-6)^(2)+(y+3)^(2)=5^(2)`

therefore

The center is the point (6,-3) and the radius is r=5 units