Question

Find the equation of the circle whose diameter has endpoints at (5, 5) and (-3, 5). Calculate the following:

a. The center of the circle.
b. The radius of the circle.
c. Write the equation of the circle in standard form: (x - h)² + (y - k)² = r² , where (h, k) represents the center of the circle, and r represents the radius.

Answer 1

The center of the circle with diameter endpoints at (5, 5) and (-3, 5) is (1, 5). The radius is 4. The equation of the circle in standard form is (x - 1)² + (y - 5)² = 16.

Step-by-step explanation:

The equation of a circle is given by ⁠(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius of the circle. To find the equation of the circle with diameter endpoints at (5, 5) and (-3, 5):

1. Calculate the center of the circle (the midpoint of the diameter). The midpoint formula is ⁠(h, k) = ((x1 + x2) / 2, (y1 + y2) / 2), leading to ⁠(1, 5)⁠ as the center.
2. Determine the radius by calculating the distance between the center and one of the endpoints of the diameter. The distance formula is r = √((x2 - x1)² + (y2 - y1)²), which gives 4 as the radius.
3. To write the equation, substitute h, k, and r into the standard form, resulting in (x - 1)² + (y - 5)² = 16.