Final answer:
To find the general equation of the circle with center (7, -4) and passing through (-5, 1), calculate the radius and then substitute the center's coordinates and radius into the circle's standard equation. The resulting equation is (x - 7)² + (y + 4)² = 13².
Step-by-step explanation:
The general equation of a circle with a center at coordinates (Cx, Cy) and radius r is given by the formula (x - Cx)2 + (y - Cy)2 = r2.
To determine the equation for the circle with a center at (7, -4) that passes through the point (-5, 1), we first need to calculate the radius r which is the distance between the center and the point on the circle.
Using the distance formula r = √((x2 - x1)2 + (y2 - y1)2),
we find r by substituting (7, -4) for (x1, y1) and (-5, 1) for (x2, y2) which results in r = √((7 - (-5))2 + (-4 - 1)2) = √(144 + 25) = √169 = 13.
The general equation of the circle is therefore (x - 7)2 + (y + 4)2 = 132.