Hi Juan G.,
The standard form equation of a circle is (x - h)2 + (y - k)2 = r2, with (h, k) the center of the circle.
For the center (-1, 10) the equation becomes:
(x - h)2 + (y - k)2 = r2
(x - [-1])2 + (y - [10])2 = r2
(x + 1)2 + (y - 10)2 = r2
We can enter the point (9, 16) into (x, y) of the equation to find r2. Finding r2 using point (9, 16) creates a radius for the circle that contains this point.
(x + 1)2 + (y - 10)2 = r2
(9 + 1)2 + (16 - 10)2 = r2
102 + 62 = r2
136 = r2
We can now write the equations of a circle centered at (-1, 10) that passes through (9, 16):
(x + 1)2 + (y - 10)2 = 136
I hope this helps, Joe.
