First slide

Pair of straight lines

Question

The equation to the pair of lines passing through origin and perpendicular to $5 x^{2} + 7 xy + y^{2} = 0$

Easy

A

$5 x^{2} - 7 xy + y^{2} = 0$
B

$x^{2} + 7 xy + 5 y^{2} = 0$
C

$5 x^{2} + 7 xy - y^{2} = 0$
D

$x^{2} - 7 xy + 5 y^{2} = 0$

Solution

The combined equation of pair of lines which are perpendicular to the pair of lines ${ax}^{2} + 2 hxy + {by}^{2} = 0$ and passing through the origin is ${bx}^{2} - 2 hxy + {ay}^{2} = 0$
Therefore, the combined equation of pair of lines which are perpendicular to the pair of lines $5 x^{2} + 7 xy + y^{2} = 0$ and passing through the origin is $x^{2} - 7 xy + 5 y^{2} = 0$ .

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