Question

If the sum of slopes of the pair of lines represented by $4x^2+2hxy-7y^2=0$ is equal to the product of the slopes, then the value of $h$ is:

• A. $–6$
• B. $–2$
• C. $–4$
• D. $4$

Answer 1

The correct option is B

$–2$

Explanation for the correct option.

Let the slopes of the pair of lines represented by $4x^2+2hxy-7y^2=0$ be $m_1\mathrm{and}{m}_2$.

The general equation representing the pair of lines is given by $a{x}^2+2hxy+b{y}^2=0$.

By comparing the given equation with the general equation, we get $a=4,h=h,\text{and}b=-7$.

The sum of the slopes will be $m_1+m_2=\frac{-2h}{b}=\frac{-2h}{-7}=\frac{2h}{7}$

The product of the slopes will be $m_1\times m_2=\frac{a}{b}=-\frac{4}{7}$

As per the given information,

$\begin{array}{rcl}\frac{2h}{7}& =& -\frac{4}{7}\\ & \Rightarrow & h=-2\end{array}$

Hence, option B is correct.