UPSC NDA Math Model Paper 2

Given: The end points of the diameter of a circle are A (3, 4) and B (5, 8).
As we know that, if (x1,y1) and (x2,y2) are the end points of the diameter of a circle then the equation of such a circle is (x−x1).(x−x2) +(y−y1)(y−y2)=0
Here, x1=3,y1=4,x2=5 and y2=8
⇒(x−3).(x−5)+(y−4).(y−8)=0
⇒x2+y2−8x−12y+47=0
So, the equation of the required circle is: x2+y2−8x−12y+47=0
Hence, option D is the correct answer.