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

Question

Consider a triangle Δ whose two sides lie on the x-axis and the line x+y+1=0. If the orthocentre of Δ is (1,1), then the equation of the circle passing through the vertices of the triangle Δ is (A) x2+y2-3 x+y=0 (B) x2+y2+x+3 y=0 (C) x2+y2+2 y-1=0 (D) x2+y2+x+y=0

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/c4f07cc73bbc452aa9767cef6aafdb8f-.png" /> Image of orthocentre about any side of the triangle lies on its circumcircle. We can observe that x2+y2+x+3 y=0 is satisfied by (-1,0) and (1,-1) both So, option (B) is the correct choice

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

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

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

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

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

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

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

x2+y2−3x+y=0

x2+y2+x+3y=0

x2+y2+2y−1=0

x2+y2+x+y=0