Question

Find center-radius: 8x^2+8x+8y^2-64y-382=0

Answer 1

recall - a circle with a center (h,k) and radius r , can look like
(x - h)^2 + (y - k)^2 = r^2

for things that look like what they gave you , usually for a book problem it is completing the square with nice whole numbers prolly

Answer 2

i would divide by 8 first

\[x^2 + x + y^2 - 8y = 382/8\]

then just turn those into a perfect square , for ax^2 + bx + ? , you can take half of b, and square that

Answer 3

x^2 + x + (1/2)^2 + y^2 - 8y + (-4)^2 = 382/8 + (1/2)^2 + (-4)^2

Answer 4

(x + 1/2)^2 + (y - 4)^2 = 382/8 + 1/4 + 16

there is your (h,k) , simplify the other side to see r^2 to get the radius