Find the center and radius for the circle, given the equation: X^2 + Y^2 + 4x - 10y = 7

Complete the squaer to get into form

(x-h) ² + (y-k) ²=r²

where the center is (h, k) and the radius is r

so

group x and y terms together

(x²+4x) + (y²-10y) = 7

take 1/2 of each coefient and square it

4/2=2, 2²=4

-10/2=-5, (-5) ²=25

add 4+25 to both sides

(x²+4x) + (y²-10y) + 4+25=7+4+25

(x²+4x+4) + (y²-10y+25) = 36

factor perfect squares

(x+2) ² + (y-5) ²=36

convert to the form

(x - (-2)) ² + (y-5) ²=6²

center is (-2,5) and radius is 6

The radius is 6 and the center is (-2,5)