Question

PLEASE SHOW ALL STEPS!!!!

Answer 1

Answer:

Center (1,3) and radius 6

Step-by-step 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.

$\frac{-2}{2} =(-1)^{2} =1$

$\frac{-6}{2} =(-3)^{2} =9$

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.