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

Answer: (A)

5/2

Answer 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 lines are parallel.

$\therefore$ Distance between them is $2\sqrt{\frac{g^{2} - ac}{a(a + b)}} = 2\sqrt{\frac{( - 3/2)^{2} - 1( - 4)}{1(1 + 3)}}$ $= 5/2$