Question

how do you find the diameter of a circle using the equation x^2+y^2+8x-22y-88=0? I need it step by step please

Answer 1

Check attached image file.

Answer 2

You can complete the square on x and y terms to find the radius:-

x^2 + 8x + y^2 - 22y - 88 = 0
(x + 4)^2 - 16 + (y - 11)^2 - 121 - 88 = 0
(x + 4)^2 + (y - 11)^2 = 121 + 88 + 16 = 225
(x + 4)^2 + (y - 11)^2 = 225
compare this with the standard form:-
( x - a)^2 + (y - b)^2  = r^2   where r = radius
So  radius = sqrt225 = 15

Diameter = 2*15  = 30 Answer