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Intercept Form of a Line

For the pair ...

Question

For the pair of lines represented by $a x^{2} + 2 h x y + b y^{2} = 0$ to be equally inclined to coordinates axes we have,

h^{2} = a b

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h + a = 0

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a = 0

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h = 0

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Solution

The correct option is D $h = 0$
$a x^{2} + 2 h x y + b y^{2} = 0$
Let the lines
$b (y - m_{1} x) y - m_{2} x) = a x^{2} + 2 h x y + b y^{2}$
$m_{1} + m_{2} = \frac{- 2 h}{b}$
and $m_{1} m_{2} = \frac{a}{b}$
If $m_{1} = m_{2}$ for equally inclined so
$\frac{- 2 h}{b} = 0 \Rightarrow h = 0$ .

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