A triangle has two of its sides along the axes, its third side touches the circle x^2 +y^2 -4x -4y - Maths - Conic Sections

Question

A triangle has two of its sides along the axes, its third side
touches the circle x^2 +y^2 -4x -4y +4= 0 Prove that locus of
circumcentre of triangle is 2(x+ y-1) =xy

Anuradha Sharma · Accepted Answer

Dear Student, Please find below the solution to the asked query First lets derive it for the general equation, x2+y2-2ax-2ay+a2= 0 and then we will put a = 2 to get the required result

Now putting a = 2 we will get 22-2×2x+y+2xy=0 2-2x+y=-xy 2 x+y-1= xy Hence proved Hope this would clear your doubt about the topic If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible Regards

A triangle has two of its sides along the axes, its third side touches the circle x^2 +y^2 -4x -4y +4= 0. Prove that locus of circumcentre of triangle is 2(x+ y-1) =xy