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Find an equation of the circle whose diameter has endpoints (1,-4) and (-3,6).

1 Answer

4 votes

Answer:


(x+1)^2+(y-1)^2=58

Explanation:

To find the equation of this circle, we must know the center and the radius.

We can find the radius by dividing the value of the distance formula by 2 (since
r=(d)/(2)):


d=√((-3-1)^2+(6-(-4))^2)=√(116)\\r=d/2=(√(116))/(2)

We can then find the center of the circle by averaging the coordinates:


(1+(-3))/(2)=-1


(-4+6)/(2)=1

Then, we substitute these values into the equation of a circle:


(x-(-1))^2+(y-1)^2=((√(116))/(2))^2\\(x+1)^2+(y-1)^2=58

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