Mathematics: Identify the center and radius from the equation of the circle given below. x^2+y^2+121-20y=-10x

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Identify the center and radius from the equation

mervindavisk

16.01.2022

Center: (-5,10)

Radius: 2

Step-by-step explanation:

The equation of the circle in center-radius form is:

(x-h)^2+(y-k)^2=r^2

Where the point (h,k) is the center of the circle and "r" is the radius.

Subtract 121 from both sides of the equation:

$x^2+y^2+121-20y-121=-10x-121\\x^2+y^2-20y=-10x-121$

Add 10x to both sides:

$x^2+y^2-20y+10x=-10x-121+10x\\x^2+y^2-20y+10x=-121$

Make two groups for variable "x" and variable "y":

(x^2+10x)+(y^2-20y)=-121

Complete the square:

Add $(\frac{10}{2})^2=5^2$ inside the parentheses of "x".

Add $(\frac{20}{2})^2=10^2$ inside the parentheses of "y".

Add 5^2 and 10^2 to the right side of the equation.

Then:

$(x^2+10x+5^2)+(y^2-20y+10^2)=-121+5^2+10^2\\(x^2+10x+5^2)+(y^2-20y+10^2)=4$

Rewriting, you get that the equation of the circle in center-radius form is:

(x+5)^2+(y-10)^2=2^2

You can observe that the radius of the circle is:

r=2

And the center is:

(h,k)=(-5,10)

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