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Can someone pls help me with this problem I don't remember how to do this

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x2 −2x + y2 − 6y = 26

Respuesta :

Luv2Teach
You need to complete the square for both the x and the y. Do this to get (x^2-2x+1) + (y^2-6y+9) = 26+1+9. Rewriting this in vertex form gives you:
(x-1)^2 + (y-3)^2 = 36. The vertex is (1,3) and the radius is 6.

The center is (1, 3)  and the radius is 6 of the circle.

What is the equation of the circle?

The equation of the circle is;

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

Where h and k are the center and r is the radius of the circle;

The given equation of circle;

[tex]\rm x^2 -2x + y^2 -6y = 26[/tex]

Convert the equation into the standard form of a circle

[tex]\rm x^2 -2x + y^2 -6y = 26\\\\Adding \ 1 \ both \ sides\\\\ x^2 -2x +1+ y^2 -6y = 26+1\\\\(x-1)^2+y^2-6y=27\\\\Adding \ 9 \ on \ both \ sides\\\\(x-1)^2+y^2-6y+9=27+9\\\\(x-1)^2+(y-3)^2=36\\\\(x-1)^2+(y-3)^2=6^2[/tex]

On comparing with the equation of a circle

h = 1, k = 3, and r = 6

Hence, the center is (1, 3)  and the radius is 6 of the circle.

Learn more about circle here;

https://brainly.com/question/23158320

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