Question

The equation of one of the line represented by the equation $pq(x^2-y^2)+(p^2-q^2)xy=0$, is

• A. $px+qy=0$
• B. $px-qy=0$
• C. $p^{2}x+q^{2}y=0$
• D. $d^{2}x-p^{2}y=0$

Answer 1

The correct option is B $px-qy=0$

Given that

the equation

$pq(x^2-y^2)+(p^2-q^2)xy=0$

$\Rightarrow pq{x}^2-pq{y}^2+p^{2}xy-q^{2}xy=0$

$\Rightarrow pq{x}^2+p^{2}xy-pq{y}^2-q^{2}xy=0$

$\Rightarrow px(qx+py)-qy(py+qx)=0$

$\Rightarrow (qx+py)(px-qy)=0$

now,

$qx+py=0,px-qy=0$

Hence,

$px-qy=0$

this is the answer.