Question

The line $x - 2y = 0$will be a bisector of the angle between the lines represented by the equation $x^{2} - 2hxy - 2y^{2} = 0$, if $h =$

• A. 1/2
• B. 2
• C. $- 2$
• D. –1/2

Answer 1

Answer: (C)

$- 2$

Answer 2

Here one equation of bisector is $x - 2y = 0.$ We know that both bisectors are perpendicular, therefore second bisector will be $2x + y = 0$because it passes through origin.

Hence the combined equations of bisectors is given by $(2x + y)(x - 2y) = 0 \Rightarrow - 2x^{2} + 3xy + 2y^{2} = 0.$

Now comparing it by $hx^{2} + 3xy - hy^{2} = 0$, we get h = –2.