If sum and product of the slope of lines represented by $4 x^{2} + 2 h x y - 7 y^{2} = 0$ are equal then $h =$

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Solution

The correct option is D $- 2$
Let $y = m_{1} x$ and $y = m_{2} x$ be the equation
Since,
$4 x^{2} + 2 h x y - 7 y^{2} = (y - m_{1} x) (y - m_{2} x)$
Solve the equation
$m_{1} m_{2} = - \frac{4}{7}$ and $m_{1} + m_{2} = \frac{2 h}{7}$
Given that,
$m_{1} + m_{2} = m_{1} m_{2}$
$\frac{2 h}{7} = - \frac{4}{7}$
$h = - 2$

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