# Find the center and radius of this equation.   X^2 + Y^2 -6X +10Y + 9 = 0

Eric Bizzell | Certified Educator

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The equation of a circle can be written as `(x-h)^2+(y-k)^2=r^2` where the center of the circle is at (h,k) on the cartesian coordinate plane, and the length of the radius is r.

We are given `x^2+y^2-6x+10y+9=0`

Rewrite as `x^2-6x+y^2+10y=-9`

Then use completing the square on the terms involving x, and the terms involving y:

`x^2-6x+9+y^2+10y+25=-9+9+25`

`(x-3)^2+(y+5)^2=25`

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The center is at (3,-5) and the radius is 5

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## Related Questions

etotheeyepi | Student

X^2 + Y^2 -6X +10Y + 9 = 0

complete the square

X^2 -6x +9 + Y^2 +10Y +25 + 9 = +9 +25

write it is squared form

(X - 3)^2 + (Y + 5)^2  = 25

so the center is (3, -5) and the radius is 5