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

(A) $5 / 2$

(B) $5 / 4$

(C) 5

(D) 0

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Best answer

SOLUTION —

$\begin{array}{l}\text { Now, } \quad \frac{a}{h}=\frac{h}{b}=\frac{g}{f} \\\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}=\frac{-3 / 2}{-3 \sqrt{3} / 2} \Rightarrow \frac{1}{\sqrt{3}}=\frac{1}{\sqrt{3}}=\frac{1}{\sqrt{3}}\end{array}$

Which is true hence lines are parallel.

$\therefore \quad d=2 \sqrt{\frac{g^2-a c}{a(a+b)}}=2 \sqrt{\frac{\frac{9}{4}+4}{4}}=\frac{5}{2}$

So, The correct option will be (A).

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