What is the equation of the circle with endpoints of the diameter of a circle are (1,-1) and (9,5)?

1 Answer
Jan 4, 2016

Answer:

#(x-5)^2+(y-2)^2=25#

Explanation:

A general circle centred at #(a,b)# and having radius #r# has equation #(x-a)^2+(y-b)^2=r^2#.

The centre of the circle would be the midpoint between the 2 diameter endpoints, ie #((1+9)/2,(-1+5)/2)=(5,2)#

The radius of the circle would be half the diameter, ie. half the distance between the 2 points given, that is

#r=1/2(sqrt((9-1)^2+(5+1)^2))=5#

Thus the equation of the circle is

#(x-5)^2+(y-2)^2=25#.