Question

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

• A. $(\frac{4}{3},-\frac{2}{3})$
• B. $(\frac{1}{2},1)$
• C. $(0,0)$
• D. $(1,1)$

Answer 1

The correct option is C $(0,0)$

Given pair of lines is
$2x^2+3xy-2y^2=0$
Here $a+b=0$
i.e. the lines are perpendicular.
So, the orthocentre lies on point of intersection of these lines. The pair of straight lines pass through the origin. Hence, the point of intersection is $(0,0)$
So, the orthocentre is $(0,0)$