A circle has a diameter with endpoints (-8, 2) and (-2, 6). What is the equation of the circle?

Solution:

It is given that

A circle has a diameter with endpoints (-8, 2) and (-2, 6).

Let us assume,

A(-8, 2) and B(-2, 6)

Then the center of the circle is midpoint A, B w(x0 ,y0)

So,

x0 = (- 8 - 2)/2 = -10/2 = -5

y0 = (2 + 6)/2 = 8/2 = 4

Equation: (x + 5)2 + (y - 4)2 = r2

r = AB/2

AB = √[(- 2 + 8)2 + (6 - 2)2]

AB = √[(36 + 16)]

AB = √52

AB/2 = √52 / 2 = √13

(x + 5)2 + (y - 4)2 = (√13)2

Therefore, the equation of the circle is (x + 5)2 + (y - 4)2 = 13.

A circle has a diameter with endpoints (-8, 2) and (-2, 6). What is the equation of the circle?

Summary:

A circle has a diameter with endpoints (-8, 2) and (-2, 6). The equation of the circle is (x + 5)2 + (y - 4)2 = 13.

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