First slide

Pair of straight lines

Question

The combined equation $5 x^{2} + 4 xy - 5 y^{2} = 0$ represents the pair of lines and those lines are

Easy

A

Perpendicular
B

Parallel
C

Coincide
D

one makes angle $45 °$ with other line

Solution

If the equation ${ax}^{2} + 2 hxy + {by}^{2} = 0$ represents a pair of perpendicular lines then $a + b = 0$
For the equation $5 x^{2} + 4 xy - 5 y^{2} = 0, a + b = - 5 + 5 = 0$
Therefore, the equation $5 x^{2} + 4 xy - 5 y^{2} = 0$ represents a pair of perpendicular lines passing through the origin.

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