If the equation $a x^{2} + 2 h x y + b y^{2} = 0$ has the one line as the bisector of angle between the coordinate axes, then

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Solution

The correct option is D

Let one line be x + y = 0 $\Rightarrow m_{1} = - 1$

and we know that $m_{1} + m_{2} = - \frac{2 h}{b}$ ..............(i)

and $m_{1} m_{2} = \frac{a}{b}$

Therefore from (ii), $m_{2} = - \frac{a}{b}$

$\Rightarrow - 1 - \frac{a}{b} = \frac{- 2 h}{b} \Rightarrow (a + b)^{2} = 4 h^{2}$ .

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Similar questions

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If the equation ax2+2hxy+by2=0 has the one line as the bisector of angle between the coordinate axes, then

The correct option is D Let one line be x + y = 0 ⇒m1=−1 and we know that m1+m2=−2hb..............(i) and m1m2=ab Therefore from (ii), m2=−ab ⇒−1−ab=−2hb⇒(a+b)2=4h2.

If the equation $a x^{2} + 2 h x y + b y^{2} = 0$ has the one line as the bisector of angle between the coordinate axes, then