Question

Find the equation of the circle passing through the points (1, 2) and (2, -1), and whose center lies on the line x - 2y + 3 = 0.

Q: Answer-Find the equation of the circle passing through the points (1, 2) and (2, -1), and whose center lies...

Let the center of the circle be h, k, and the equation of the circle be x - h2 y - k2 r2. Since the circle passes through 1, 2 and 2, -1 1 - h2 2 - k2 r2 and 2 - h2 -1 - k2 r2. Also, the center lies on the line x - 2y 3 0, so h - 2k 3 0. Solve this system of three equations to find h, k, and r. After solving h 1, k -2, and r2 8. The equation of the circle is x - 12 y 22 8.