Question

Write an equation for a circle with a diameter that has endpoints at (7, –4) and (1, –10). Round to the nearest tenth if necessary.

Answer 1

The standard form for the equation of a circle is :

(x−h)^2+(y−k)^2=r2 ----------- EQ(1)
where handk are the x and y coordinates of the center of the circle and r is the radius.
The center of the circle is the midpoint of the diameter.
So the midpoint of the diameter with endpoints at (7,-4)and(1,-10) is : ((7+(1))/2,(-4+(-10))/2)=(4,-7)
So the point (4,-7) is the center of the circle. Now, use the distance formula to find the radius of the circle:
r^2=(7−(4))^2+(-4−(-7))^2=9+9=18
⇒r=√18
Subtituting h=4, k=-7 and r=√18 into EQ(1) gives : (x-4)^2+(y+7)^2=18