Question

14. The diameter of a circle has endpoints A(-8, -5) and B(4, 11). Write the equation of the circle. (**hint: you must find the center and radius)

Answer 1

x² + y² - 12x - 16y = 280

Explanation:

The diameter of a circle has endpoints A(-8,-5) and B(4,11)

The equation of a circle is given by: (x - a)² + (y - b)² = r² , Where x and y are points on the circle and (a, b) is the center of the circle. r is the radius.

To find the center of the circle:

Center = (
`(4 - -8)/(2)`,
`(11 - -5)/(2)`) = (6, 8)

The length of the diameter is the square root of change in y squared plus change in x squared.

The length of the diameter squared = (11 - -5)² + (4 - -8)² = 400

The diameter is
`\sqrt[]{400}` = 20 units

Taking another point (x,y) on the circle,

The equation of the circle will be:

(x - 6)² + (y - 8)² = 20²

Simplifying this gives;

x² - 12x + 36 + y² - 16y + 84 = 400

x² + y² - 12x - 16y = 400 - 84 - 36

x² + y² - 12x - 16y = 280