Final answer:
The correct equation of the circle with center at (5,-7) and passing through (-5,1) is (x - 5)² + (y + 7)² = 169, after calculating the radius using the distance formula.
Step-by-step explanation:
The student has asked for the completion of the equation of a circle with a center at (5,-7) that passes through the point (-5,1). To find the correct equation, we need to determine the radius of the circle which can be calculated using the distance formula: √[(x2 - x1)² + (y2 - y1)²], where (x1, y1) is the center of the circle and (x2, y2) is a point on the circle.
Substituting the given points into the distance formula, we get the radius r as: √[(-5 - 5)² + (1 - (-7))²] = √[(-10)² + (8)²] = √[100 + 64] = √164 = 13.
Now we insert the center coordinates and the radius into the standard form of the circle equation: (x - h)² + (y - k)² = r², where h and k are the x and y coordinates of the center, respectively. The correct equation of the circle is therefore: (x - 5)² + (y + 7)² = 169.