Question

The orthocentre of the triangle formed by the lines $x^2-3y^2=0$ and the line $x=a$ is

• A. $\left(\frac{a}{3},0\right)$
• B. $\left(\frac{2a}{3},0\right)$
• C. $(a,0)$
• D. $\left(\frac{4a}{3}0\right)$

Answer 1

Answer: (B)

$\left(\frac{2a}{3},0\right)$

$x^2-3y^2=0$
$x=\sqrt{3}y$ and $x=-\sqrt{3}y$
$\Delta OAB$ is equilateral triangle
$\therefore$ orthocentre and centroid of $\Delta OAB$ concides

$\therefore$ orthocentre $=(\frac{29}{3},0)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$