Question

$O(0,0),A(1,2),B(3,4)$ are the vertices of $△OAB$. The joint equation of the altitude and median drawn from $O$ is

• A. $x^2+7xy-y^2=0$
• B. $x^2+7xy+y^2=0$
• C. $3x^2-xy-2y^2=0$
• D. $3x^2+xy-2y^2=0$

Answer 1

The correct option is D $3x^2+xy-2y^2=0$

Equation of median $OD=y=mx\Rightarrow 3=2m$
$\Rightarrow m=\frac{3}{2}$
$\therefore y=\frac{3}{2}x\Rightarrow 3x-2y=0$
Slope of $AB=\frac{2}{2}=1\Rightarrow$ Slope of $OP=-1$
Equation of $OP\Rightarrow y=-x\Rightarrow x+y=0$
Joint equation of $OP$ and $OD\Rightarrow (x+y)(3x-2y)=0$
$\Rightarrow 3x^2+xy-2y^2=0$