Question

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

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

Answer 1

The correct option is A

${90}^{°}$

Explanation for the correct option:

Given equation can be simplified as

$$\begin{gathered} x^2-y^2-2y-1=0 \\ {x}^2-(y^2+2y+1)=0 \\ {x}^2-{(y+1)}^2=0 \end{gathered}$$

On equating this with the standard equation $a{x}^2+2bxy+b{y}^2=0$ we get:

$$\begin{gathered} a=1 \\ h=0 \\ b=-1 \end{gathered}$$

We know that, the formula for the angle between two lines is

$$\begin{gathered} \tan \theta =\frac{2\sqrt{b^2-ab}}{a+b} \\ \Rightarrow \theta ={\tan }^{-1}\left(\frac{2\sqrt{h^2-ab}}{a+b}\right) \\ ={\tan }^{-1}\left(\frac{2\sqrt{-\left(1\right)(-1)}}{1-1}\right) \\ ={\tan }^{-1}\left(\frac{1}{0}\right) \\ ={90}^{°} \end{gathered}$$

Hence, option (A) is the correct answer.