Question

Consider a triangle $\Delta$ whose two sides lie on the $x$-axis and the line $x+y+1=0$. If the orthocentre of $\Delta$ is $(1,1)$, then the equation of the circle passing through the vertices of the triangle $\Delta$ is

• A. $x^{2}+y^{2}-3 x+y=0$
• B. $x^{2}+y^{2}+x+3 y=0$
• C. $x^{2}+y^{2}+2 y-1=0$
• D. $x^{2}+y^{2}+x+y=0$

Answer 1

Answer: (B)

Image of orthocentre about any side of the triangle lies on its circumcircle.
We can observe that
$x^{2}+y^{2}+x+3 y=0$ is satisfied by $(-1,0)$ and $(1,-1)$ both
So, option (B) is the correct choice