Question

Using the follow equation, find the center and radius of the circle. You must show all work and calculations to recieve credit. x^2 -2x + y^2 - 6y = 26 (10 points)

Answer 1

Using the follow equation, find the center and radius of the circle. You must show all work and calculations to recieve credit. x^2 -2x + y^2 - 6y = 26

we have the equation

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

group terms

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

Complete the squares

$(x^2-2x+1)+(y^2-6y+9)=26+1+9$$(x^2-2x+1)+(y^2-6y+9)=36$

REwrite as perfect squares

$(x^{}-1)^2+(y-3)^2=6^2$

the center is the point (1,3) and the radius is 6 units