Question

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.

Answer 1

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