Which equation represents a circle

A. x2 – 2x – 24 = 0

B. x2 – 2x – y – 23 = 0

C. y2 – 2x – 2y – 78 = 0

D. x2 + y2 – 2x – 2y – 34 = 0

E. y2 – 2y – 23 = 0

The answer is D. x2 + y2 – 2x – 2y – 34 = 0

To see it, complete the square for both variables:
x2 + y2 – 2x – 2y – 34 = 0 =>
(x^2 - 2x) + (y^2 - 2y) = 34 =>
(x^2 - 2x + 1) + (y^2 - 2y + 1) = (34 + 1 + 1) =>

(x-1)^2 + (y-1)^2 = 36
This is the standard form for a circle centered at (1,1) with radius 6

:-D