Question

PLEASE SHOW ALL STEPS!!!!

find the center and radius of the circle.

x2 −2x + y2 − 6y = 26

Answer 1

Center (1,3) and radius 6

Explanation:

We must complete the square to find the center and radius of the circle.

First make sure the x and y squared terms have 1 as their coefficients. We also make sure x and y terms together.

`x^2-2x+y^2-6y=26`

We now create space between the x and y terms with parenthesis.

`(x^2-2x)+(y^2-6y)=26`

We complete the square by taking the middle terms -2x and the -6y - divide each and square them.

`(-2)/(2) =(-1)^(2) =1`

`(-6)/(2) =(-3)^(2) =9`

We add the squares to both sides.

`(x^2-2x+1)+(y^2-6y+9)=26+1+9`

Simplify.

`(x^2-2x+1)+(y^2-6y+9)=36`

And write the quadratics in factored form.

`(x-1)^(2) +(y-3)^(2) =36`

The center is (h,k) or (1,3). The radius is the square root of 36 which is 6.