Question

Distance between the lines represented by the equation $x^2+2\sqrt{3}xy+3y^2-3x-3\sqrt{3}y-4=0$ is

• A. 5/2
• B. 5/4
• C. 5
• D. 0

Answer 1

The correct option is A

5/2

First check for parallel lines

i.e., $\frac{a}{h}=\frac{h}{b}=\frac{g}{f}\Rightarrow \frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}=\frac{\frac{-3}{2}}{\frac{-3\sqrt{3}}{2}}$

which is true, hence line are parallel.Applying formula for distance between two parallel straight lines, the required distance is $2\sqrt{\frac{g^2-ac}{a(a+b)}}=2\sqrt{\frac{\frac{9}{4}+4}{4}}=\frac{5}{2}$