First slide

Pair of straight lines

Question

The equation of the pair of lines passing through the origin and having slope $m \in I$ (I is integer) for which equation $(x - 3) (x + m) + 1 = 0$ has integral roots is

Moderate

A

$y^{2} - 6 x y - 5 x^{2} = 0$
B

$y^{2} - 6 x y + 5 x^{2} = 0$
C

$y^{2} + 6 x y - 5 x^{2} = 0$
D

$y^{2} + 6 x y + 5 x^{2} = 0$

Solution

$x - 3 = 1$ and $x + m = - 1 \Rightarrow x = 4, m = - 5$
$x - 3 = 1 a n d x + m = 1 \Rightarrow x = 2, m = - 1$
equation of pair of lines $y^{2} - (m_{1} + m_{2}) x y + m_{1} m_{2} x^{2} = 0$
$\Rightarrow y^{2} + 6 x y + 5 x^{2} = 0$

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