First slide

Pair of straight lines

Question

If $2 x^{2} + 3 xy + {ky}^{2} - 5 x + 5 y + 7 = 0$ represents a pair of perpendicular lines, $k =$

Easy

A

1
B

2
C

-2
D

-1

Solution

If the equation ${ax}^{2} + 2 hxy + {by}^{2} = 0$ represents a pair of perpendicular lines then $a + b = 0$
For the equation $2 x^{2} + 3 xy + {ky}^{2} - 5 x + 5 y + 7 = 0$
$\begin{matrix} k + 2 = 0 \\ k = - 2 \end{matrix}$
Therefore, $k = - 2$

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