Which of the following points lies on the circle whose center is at the origin and whose radius is 13? (-5, 12) (, ) (6, -7)

The equation of a circle is defined by (x – h)² + (y – k)² = r² with the center being at (h, k) and with radius r. So for this circle with center at (0, 0) and r = 13 the equation is x² + y² = 169.
Then we plug in the ordered pairs:
(-5, 12)
(-5)² + (12)² = 169
25 + 144 = 169 is true. 

The answer is (-5, 12). Hope that helps.

Where are the calculations?

I’m sure you could google it. my profile picture might