Answer:
Radius = 5
center is (19,-1)
[tex](x-19)^2(y+1)^2= 25[/tex]
Step-by-step 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
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]=\sqrt{\left(19-19\right)^2+\left(-6-4\right)^2}=10[/tex]
diameter = 10
radius = diameter divide by 2
Radius = 5
midpoint is the center of the circle
[tex]\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(\frac{19+19}{2},\:\frac{-6+4}{2}\right)[/tex]
(19,-1)
Equation of the circle
[tex](x-h)^2(y-k)^2= r^2[/tex]
h,k is the center and r is the radius
h=19 and k=-1 , r=5
[tex](x-19)^2(y+1)^2= 25[/tex]
