question_answer

The circumcentre of a triangle formed by the lines\[xy+2x+2y+4=0\]and\[x+y+2=0\], is

A) \[(0,\,\,-1)\]                      

B) \[(-1,\,\,0)\]

C) \[(1,\,\,1)\]                        

D)        \[(-1,\,\,-1)\]

Correct Answer: D

Solution :

Given lines are                 \[xy+2x+2y+4=0\]                           ... (i) and        \[x+y+2=0\]                                       ... (ii) From Eqs. (i) and (ii), we get                 \[xy=0\] \[\Rightarrow \]               \[x=y=0\] \[\therefore \]Vertices of triangle are \[(-2,\,\,0),\,\,(0,\,\,0),\,\,(0,\,\,-2)\]. In a right angled triangle circumcentre is the midpoint of hypotenuse. \[\therefore \]Point (-1,-1) is the required coordinate of the circumcentre.