Question

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

• A. a = 9; h = -4
• B. a + h = 6
• C. angle between the lines represented by first pair is $\frac{\pi }{4}$
• D. all of these

Answer 1

The correct option is A a = 9; h = -4

Let $m_1$ and $m_2$ be the slope of lines of first pair

$\Rightarrow m_1$ and $\Rightarrow m_2$ be the slope of lines of second pair

Compairing pair of lines (y-$\Rightarrow m_{1}x$ ) (y-$\Rightarrow m_{2}x$ ) with $y^2+2hxy-9x^2=0$

and pair of lines (y-$\Rightarrow m_{1}x$ ) $y+\frac{1}{m_2}x$ with $a{y}^2+10xy+x^2=0$

we get $m_1=-1and{m}_2=9\Rightarrow a=9andh=-4$