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