Respuesta :
Answer: 4) The center is located at (1, 3), and the radius is 6
Step-by-step explanation:
Solve the general equation of the circle.
x^2 -2x +1+ y^2-6y+9= 26+1+9 (x-1)^2+(y-3)^2=36=6^2
Hence, the coordinates of the center (1,3) And the radius will be 6
The center is located at (1,3) and the radius is 6.
What is center of the circle?
"The center is the point from which all of the points on the circle are the same distance."
What is radius of the circle?
"The radius is the exact distance from the center to any point on the circle."
We have
[tex]x^{2} -2x+y^{2}-6y = 26\\[/tex]
Add 1 and 9 on both sides of equation
⇒[tex]x^{2} -2x+1+y^{2}-6y+9 = 26+1+9[/tex]
⇒[tex](x-1)^{2} +(y-3)^{2}= 36[/tex]
⇒[tex](x-1)^{2}+(y-3)^{2}=6^{2}[/tex].......(1)
We know the Standard form of equation of the circle
[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]
By comparing the standard form and equation (1)
Center (h, k) = (1, 3) and radius is 6
Hence, The center is located at (1,3) and the radius is 6.
Learn more about circle here
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