The endpoints of a diameter of a circle are located at #(5,9)# and #(11, 17)#. What is the equation of the circle?

Question

15298 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-03T09:38:43

#x^2+y^2-16x-26y+208=0#

If endpoints of a diameter of a circle are located at #(5,9)# and #(11,17)#,

center is given by the midpoint of line joining them i.e. #((5+11)/2,(9+17)/2)# i.e. #(8,13)#.

Radius is distance between #(8,13)# and #(5,9)# i.e. #sqrt((8-5)^2+(13-9)^2)=sqrt(9+16)=sqrt25=5#.

Hence equation of circle is

#(x-8)^2+(y-13)^2=25# or

#x^2-16x+64+y^2-26y+169=25# or

#x^2+y^2-16x-26y+208=0#