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Pair of Lines

The lines joi...

Question

The lines joining the origin to the point of intersection of $3 x^{2} + m x y - 4 x + 1 = 0$ and $2 x + y - 1 = 0$ are at right angles. Then all possible values of $m$ lie in the interval

R

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[1, 2]

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ϕ

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(1, 2]

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Solution

The correct option is A $R$
Equation of the lines joining the origin to the points of intersection of the given lines is
$3 x^{2} + m x y - 4 x (2 x + y) + 1 (2 x + y)^{2} = 0$
(by homogenization)
$\Rightarrow x^{2} - m x y - y^{2} = 0$
which are perpendicular for all values of $m .$

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