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The diameter of a circle has endpoints P(-6,-11 ) and Q(4, 7). Write an equation for the circle. Be sure to show and explain all work. Thank you!

Sagot :

Answer:

(x + 1)^2 + (y + 2)^2 = 106

Step-by-step explanation:

The formula for a circle is

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

Where (h, k) is the center of the circle and r is the raadius

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The center is the midpoint of the diameter end points

(h, k) = ( (-6 + 4)/2 , (-11 + 7)/2 )

(h, k) = (-1, -2)

The radius is the distance from the center to an endpoint

Using (h, k) and Q

r^2 = (4 - -1)^2 + (7 - -2)^2

r^2 = 5^2 + 9^2

r^2 = 106

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Plug into the circle formula

(x + 1)^2 + (y + 2)^2 = 106

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