Question

The equation $a^2{x}^2+2h(a+b)xy+b^2{y}^2=0$ and $a{x}^2+2hxy+b{y}^2=0$ represent

• A. two pairs of perpendicular straight lines
• B. two pairs of parallel straight lines
• C. two pairs of straight lines which are equally inclined to each other
• D. None of these

Answer 1

Answer: (C)

two pairs of straight lines which are equally inclined to each other

$a{x}^2+2hxy+b{y}^2=0$
Equation of the angle bisectors is given by
$\frac{x^2-y^2}{a-b}=\frac{xy}{h}$ ...(i)
For $a^2{x}^2+2h(a+b)xy+b^2{y}^2=0$
The equations of the angle bisector is given by
$\frac{x^2-y^2}{a^2-b^2}=\frac{xy}{h(a+b)}$
$\frac{x^2-y^2}{a-b}=\frac{xy}{h}$ ...(ii)
Since (i) is equal to (ii), the above lines are equally inclined to each other.