Question

The pair of lines joining origin to the intersection of the curve $\frac{x^{2}}{a^{2}}$ + $\frac{y^{2}}{b^{2}}$ = 1 by the line lx + my + n = 0 are coincident if-

• A. a²l² + b² m² = n²
• B. $\frac{a^{2}}{\mathcal{l}^{2}} + \frac{b^{2}}{m^{2}} = \frac{1}{n^{2}}$
• C. $\frac{\mathcal{l}^{2}}{a^{2}} + \frac{m^{2}}{b^{2}}$ = n²
• D. None of these

Answer 1

Answer: (A)

a²l² + b² m² = n²

Answer 2

lx + my + n = 0 ̃ $\frac{\mathcal{l}x + my}{- n}$ = 1

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 = $\frac{\mathcal{l}x + my}{- n}$

$\left( \frac{n^{2}}{a^{2}} - \mathcal{l}^{2} \right)$ x² + $\left( \frac{n^{2}}{b^{2}} - m^{2} \right)$y² – 2mxy = 0

This represent a pair of coincident lines if

l² m² – $\left( \frac{n^{2}}{a^{2}} - \mathcal{l}^{2} \right)$ $\left( \frac{n^{2}}{b^{2}} - m^{2} \right)$ = 0

$\frac{n^{4}}{a^{2}b^{2}}$ = $\frac{n^{2}m^{2}}{a^{2}}$ + $\frac{n^{2}\mathcal{l}^{2}}{b^{2}}$ ̃ a²l² + b²m² = n²