Question

Write an equation for a circle with a diameter that has endpoints at (–10, 1) and (–8, 5). 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 (−10,1)and(−8,5) is : ((−10+(−8))/2,(1+5)/2)=(−9,3)
So the point (−9,3) is the center of the circle. Now, use the distance formula to find the radius of the circle:
r^2=(−10−(−9))^2+(1−3)^2=1+4=5
⇒r=√5
Subtituting h=−9, k=3 and r=√5 into EQ(1) gives : (x+9)^2+(y−3)^2=5