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

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$x^{2} + y^{2} + 2 y - 1 = 0$

$x^{2} + y^{2} - 3 x + y = 0$

$x^{2} + y^{2} + x + y = 0$

$x^{2} + y^{2} + x + 3 y = 0$

answer is B.

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Detailed Solution

Image of orthocentre about any side of the triangle lies on its circucircle.
Question Image
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.

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