Question

6. Two points in the plane, ????(19,4) and ????(19,−6), represent the endpoints of the diameter of a circle.

a. What is the center of the circle?
b. What is the radius of the circle?
c. Write the equation of the circle.

Answer 1

Radius = 5

center is (19,-1)

`(x-19)^2(y+1)^2= 25`

Explanation:

Two points in the plane, (19,4) and (19,−6), represent the endpoints of the diameter of a circle.

Distance between the points is calculated using formula

`d=√(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

`=√(\left(19-19\right)^2+\left(-6-4\right)^2)=10`

diameter = 10

radius = diameter divide by 2

Radius = 5

midpoint is the center of the circle

`\left((x_2+x_1)/(2),\:\:(y_2+y_1)/(2)\right)`

`\left((19+19)/(2),\:(-6+4)/(2)\right)`

(19,-1)

Equation of the circle

`(x-h)^2(y-k)^2= r^2`

h,k is the center and r is the radius

h=19 and k=-1 , r=5

`(x-19)^2(y+1)^2= 25`