Question

Find the standard equation of a circle that passes through the point (−1, 1) with center (2, 3).

Answer 1

The equation of a circle is
  (x-h)² + (y-k)² = r²
for center (h, k) and radius r. Of course, the radius can be computed by putting the point in the equation.
  (x-2)² + (y-3)² = (-1-2)² + (1-3)² = 9+4 = 13

The standard equation of the circle is (x-2)² + (y-3)² = 13.