Question

If ${}^{\prime }{\theta }^{\prime }$ is the angle between the lines $a{x}^2+2hxy+b{y}^2=0$, then angle between $x^2+2xysec\theta +y^2=0$ is

• A. $\theta$
• B. $2\theta$
• C. $\frac{\theta }{2}$
• D. $3\theta$

Answer 1

The correct option is A $\theta$

Angle between the lines $a{x}^2+2hxy+b{y}^2=0$ is $\tan \theta =\left|\frac{2\sqrt{h^2-ab}}{a+b}\right|$
For $x^2+2xysec\theta +y^2=0$
$h=sec\theta ,a=b=1$
$\therefore \tan \varphi =\left|\frac{2\sqrt{se{c}^2\theta -1}}{1+1}\right|$
$=\frac{2\tan \theta }{2}=\tan \theta$
$\therefore$ Angle between $x^2+2xysec\theta +y^2=0$ is $\theta$.