Question

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

• A. $(0,0)$
• B. $(-2,-2)$
• C. $(-1,-1)$
• D. $(-1,-2)$

Answer 1

Answer: (C)

The given equation $xy+2x+2y+4=0$ 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 $\Delta ABC$ is right angled triangle with right angle at $C$.
Hence, centre of the circumcircle is the mid point of $AB$ whose coordinates are $(-1,-1)$