Question

The distance between the pair of parallel lines $ {{x}^{2}}+4xy+4{{y}^{2}}+3x+6y-4=0 $ is :

• A. $ \sqrt{5} $
• B. $ \frac{2}{\sqrt{5}} $
• C. $ \frac{1}{\sqrt{5}} $
• D. $ \frac{\sqrt{5}}{2} $
• E. $ \sqrt{\frac{5}{2}} $

Answer 1

Answer: (A)

$ \because $ The given equation of pair of parallel lines is $ {{x}^{2}}+4xy+4{{y}^{2}}+3x+6y-4=0 $
Here, $ a=1,b=4g=\frac{3}{2} $ and $ c=-4. $
Then, required distance $ =2\sqrt{\frac{{{g}^{2}}-ac}{a(a+b)}} $
$ =2\sqrt{\frac{\frac{9}{4}+4}{5}}=\frac{2.\sqrt{16+9}}{2.\sqrt{5}} $
$ =\frac{2\sqrt{25}}{2\sqrt{5}}=\frac{5}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}} $
$ =\sqrt{5} $