What is the equation of the circle passing through the point (6,5) and centered at (3.-4)?

(x - 3)² + (y + 4)² = 90 or [3√10)²

Step-by-step explanation:

We need to calculate the radius of this circle.  To do this we calculate the distance from the center (3, -4) to the point (6, 5).  

As we move from (3, -4) to (6, 5), x (the run) increases by 3 and y (the run) increases by 9.  Thus, the distance between these points, according to the Pythagorean Theorem, is

r = √[3² + 9²], or r = √90, or r = 3√10.

Using the standard equation of the circle, (x - h)² + (y - k)² = r², we obtain

(x - 3)² + (y + 4)² = 90 or [3√10)²