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Vilka [71]
2 years ago
9

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

Mathematics
1 answer:
dusya [7]2 years ago
8 0

Answer:

Radius = 5

center is (19,-1)

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

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

d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

=\sqrt{\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(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)

\left(\frac{19+19}{2},\:\frac{-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

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