Question

Create the equation of a circle that passes through (2, 2) with center (5, 6) using the correct operations and values below.+-24562536

Answer 1

To create the equation of a circle through (2, 2) with center (5, 6), calculate the radius and use the standard circle equation. The resulting equation is (x - 5)² + (y - 6)² = 25.

Step-by-step explanation:

To create the equation of a circle that passes through the point (2, 2) with center at (5, 6), we use the standard form of the equation of a circle, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is the radius of the circle.

First, we need to determine the radius of our circle by calculating the distance between the center (5, 6) and the point on the circle (2, 2).

The distance formula is √((x_2 - x_1)² + (y_2 - y_1)²), so we get r = √((2 - 5)² + (2 - 6)²) = √(9 + 16) = √25 = 5.

Now, we can substitute the center's coordinates and the radius into the circle's standard equation: (x - 5)² + (y - 6)² = 5², which simplifies to (x - 5)² + (y - 6)² = 25.