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  4. The circumcentre of the triangle formed by the lines xy + 2x + 2y + 4 = 0 and x + y + 2 = 0 is

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Q. The circumcentre of the triangle formed by the lines $ xy + 2x + 2y + 4 = 0 $ and $ x + y + 2 = 0 $ is

MHT CETMHT CET 2007

Solution:

The given equation $xy+2 x+2 y+4=0$ can be rewritten as $(x+2)(y+2)=0$ or $x+2=0$ $y+2=0$
And also given that $x+y+2=0$
On solving the above equations, we get
$A(-2,0), B(0,-2), C(-2,-2)$
It is clearly that $\Delta A B C$ is right angled triangle with right angle at $C$.
Hence, centre of the circumcircle is the mid point of $A B$ whose coordinates are $(-1,-1)$