Question

find the angle between the lines 2x²+2√17xy+4y²=0​

Answer 1

Step-by-step explanation:

Let the slope of pair of lines represented by the equation $2{x}^{2}+2\sqrt{17}xy + 4y^{2}$ be $m_{1} & m_{2}$

Now,

$m_{1} + m_{2} = - \sqrt{17} \implies m_{1} - m_{2} = 3\\ m_{1}m_{2} = 2$

Required angle

$\tan( \theta) = \frac{ | m_{1} - m_{2} | }{1 +m_{1}m_{2}}$

$\tan( \theta) = \frac{ 3 }{1 +2}$

$\implies \: \theta = \frac{\pi}{4}$