Question

the center of the circle with the equation x^2+y^2+8x-10y= -5 (CAN SOMEONE HELP ME WITH THIS PLEASE)

Answer 1

Complete the square for both x and y

x^2+y^2+8x-10y= -5

x^2+8x+y^2-10y= -5

x^2+8x+16+y^2-10y= -5+16

x^2+8x+16+y^2-10y+25= -5+16+25

(x^2+8x+16)+(y^2-10y+25)= 36

(x+4)^2 + (y-5)^2 = 36

(x-(-4))^2 + (y-5)^2 = 6^2

The equation is now in the form (x-h)^2+(y-k)^2=r^2, which is a circle with center (h,k) and has a radius of r

Since h = -4 and k = 5, the center of this circle is (-4, 5)

Answer 2

if given an equation of circle : x^2+y^2+Ax+By+C=0
h=-A/2 = -8/2 = -4
k=-B/2 = -(-10)/2 = 5