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)

x² + y² - 12x - 16y = 280

Step-by-step 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 = (,) = (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 = 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

the correct answer is option c.   3

step-by-step explanation:

points to remember

equation of the line with coordinates (x₁, y₁) and (x₂, y₂) is given by,

slope m = (y₂ - y₁)/(x₂ - x₁)

from the figure we can see a line with two coordinates given

to find the slope of given line

here   (x₁, y₁)   = (-1, -1 ) and (x₂, y₂) = (1, 5)

slope m = (y₂ - y₁)/(x₂ - x₁)

  = (5 - -1)/(1 - -1)

  = (5 + 1)/(1 + 1)

  = 6/2 = 3

therefore the correct answer is option c.   3