Question bank/JEE Main/Mathematics

If pair of lines y^2 + 2hxy - 9x^2 = 0 and another pair of
lines given by ay^2 + 10xy + x^2 = 0 have
exactly one line common and other lines represented by them are
perpendicular, then

Aa + h = 3Ba + h = 6Cangle between the lines represented by first pair isDa = 9, h = -4;qXe ay^2 + 10xy + x^2 = 0

Show answer and solution▾

[IMAGE] $m_{1} + m_{2} = - 2h$ $m_{1} - \frac{1}{m_{2}} = - \frac{10}{a}$
$m_{1}m_{2} = - 9$
$- \frac{m_{1}}{m_{2}} = \frac{1}{a} \Rightarrow m_{2} = 9$
$m_{1} = - \frac{9}{a}$
On solving gy djus ij: a = 9, h = - 4

Source: Grass-G / M-26 Mathematics Paper 1 15 Jan.docx