What is the equation of the circle centered at (−2, 4) and passing through (2, 8)?




(x – 2)² + (y + 4)² = 32


(x + 2)² + (y – 4)² = 16


(x + 2)² + (y – 4)² = 32


(x – 2)² + (y + 4)² = 16

1 answer

The correct equation is: (x + 2)² + (y - 4)² = 32

The center of the circle is (-2, 4), so the equation will be in the form (x - a)² + (y - b)² = r², where (a, b) is the center of the circle and r is the radius.

The distance between the center (-2, 4) and the point on the circle (2, 8) can be calculated using the distance formula: sqrt((2 - (-2))² + (8 - 4)²) = sqrt(16 + 16) = sqrt(32) = 4√2. This distance is equal to the radius of the circle.

Substitute the values into the equation: (x + 2)² + (y - 4)² = (4√2)² = 32

Therefore, the equation of the circle centered at (-2, 4) and passing through (2, 8) is (x + 2)² + (y - 4)² = 32.