The equation $x^{2} + k_{1} y^{2} + k_{2} x y = 0$ represents a pair of perpendicular lines, if

$k_{1} = - 1$

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$k_{1} = 2 k_{2}$

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$2 k_{1} = k_{2}$

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None of these

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Solution

The correct option is A
$k_{1} = - 1$

Explanation for the correct option:
Find the value of $k_{1}$ .
We know that, a pair of straight lines represent perpendicular lines, if the sum of coefficient of $x^{2}$ and coefficient of $y^{2}$ is equal to zero.
The equation $x^{2} + k_{1} y^{2} + k_{2} x y = 0$ of pair of perpendicular liines is given.
So,
$1 + k_{1} = 0 \Rightarrow k_{1} = - 1$
Therefore, the value of $k_{1}$ is $- 1$ .
Hence, the option $A$ is correct .

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