Under what condition will the lines $m^{2} x + n y - 1 = 0$ and $n^{2} x - m y + 2 = 0$ be perpendicular?

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Question

This question was previously asked in

NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)

Answer 1

Calculation:

Given,

Line 1: $m^2x + ny - 1 = 0 $

Line 2: $n^2x - my + 2 = 0 $

Slope of Line 1, $m_1 = -\dfrac{m^2}{n}$

Slope of Line 2, $m_2 = \dfrac{n^2}{m}$

For perpendicular lines, $m_1 \times m_2 = -1$.

$\frac{-m^2}{n} \times \frac{-n^2}{m} = -1$

mn -1 = 0

Hence, the correct answer is Option 1.

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