Question

The angle between the pair of straight lines $x^2-y^2-2y-1=0$ is

• A. ${90}^o$
• B. ${60}^o$
• C. ${75}^o$
• D. ${36}^o$

Answer 1

The correct option is A ${90}^o$

Given, the equation of pair of straight Lines

$x^2-y^2-2y-1=0$

$x^2-(y^2+2y+1)=0$

$x^2-(y+1{)}^2=0$

Equating with the standard equation

$a{x}^2+2bxy+b{y}^2=0$

$a=1$

$h=0$

$b=-1$

$\theta ={\tan }^{-1}\left(\frac{2\sqrt{b^2-ab}}{a+b}\right)$

$={\tan }^{-1}\left(\frac{2\sqrt{-\left(1\right)(-1)}}{1-1}\right)$

$={\tan }^{-1}\left(\frac{1}{0}\right)$

$\therefore \theta ={90}^{\circ }$