If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. first, find the midpoint of the diameter, which is the center of the circle. then find the radius, which is the distance from the center to either endpoint of the diameter. finally use the center-radius form to find the equation. find the center-radius form for the circle having the endpoints left parenthesis 5 comma 2 right parenthesis and left parenthesis negative 7 comma 4 right parenthesis of a diameter.

Given

Endpoints of the diameter (5,2) and (-7,4)

Step One

Find the center

Center = (x2 + x1)/2 , (y2 + y1)/2

x2 = -7; x1 = 5; y2 = 4; y1 = 2

Center = (-7 + 5)/2 ; (4 + 2)/2;

Center = (-1 , 3)

Step Two

Find the radius squared using the distance formula. Use (5,2) as the second point. The other point is the center.

Distance squared = (5 - - 1)^2 + (2 - 3)^2

Distance squared = ( 6)^2 + (-1 )^2

Distance squared = 37

Step Three

State the circle's formula

(x - - 1 )^2 + (y - 3)^2 = 37

(x + 1)^2 + (y - 3)^2 = 37

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step-by-step explanation:

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