Question

The equation of one of the lines 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. $q^{2}x–p^{2}y=0$

Answer 1

The correct option is B

$px–qy=0$

Explanation For the correct option:

Finding the equation of line:

The given equation

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

Expanding this equation, we get

$$\begin{gathered} pq{x}^2–pq{y}^2+p^{2}xy–q^{2}xy=0 \\ pq{x}^2–q^{2}xy+p^{2}xy–pq{y}^2=0 \\ \text{Factorising by taking a common factor}(px–qy) \\ qx(px–qy)+py(px–qy)=0 \\ (px–qy)(qx+py)=0 \\ \text{Thus, the factors are} \\ (px–qy)=0\text{and}(qx+py)=0 \end{gathered}$$

Therefore, the equations of the line is $px–qy=0$

Hence, option (B) is the correct answer.