Question

The lines $33y^2-136xy+135x^2=0$ are equally inclined to

• A. $x+2y=0$
• B. $2x-y-7=0$
• C. $3x+2y-7=0$
• D. $x+y=1$

Answer 1

The correct option is A $x+2y=0$

We have,

$33y^2-136xy+135x^2=0$

$135x^2-136xy+33y^2=0$

$\frac{x^2-y^2}{a-b}=\frac{xy}{h}$

$a=135,b=33,h=-68$

$\frac{x^2-y^2}{{10}^2}=\frac{xy}{-68}$

$2x^2+3xy-2y^2=0$

$2x^2+4xy-xy-2y^2=0$

$2x(x+2y)-y(x+2y)$

$(2x-y)(x+2y)=0$

$\therefore 2x-y=0$

$2x=y$

$\therefore x+2y=0$

Hence this is the answer,