If the equation, \(x^2+2 \sqrt{2} x y+2 y^2+4 x+4 \sqrt{2} y+1=0\) represents a pair of straight lines which…
If the equation, \(x^2+2 \sqrt{2} x y+2 y^2+4 x+4 \sqrt{2} y+1=0\) represents a pair of straight lines which are parallel to each other. Find the distance between them is
4 units
2 units
\(2 \sqrt{3}\) units (d)
\(4 \sqrt{3}\) units
Solution
Given equation of pair of parallel straight lines
\(\begin{aligned}
& x^2+2 \sqrt{2} x y+2 y^2+4 x+4 \sqrt{2} y+1=0 \\
& (x+\sqrt{2} y+2+\sqrt{3})(x+\sqrt{2} y+2-\sqrt{3})=0
\end{aligned}\)
Now, distance between parallel lines \(x+\sqrt{2} y+2+\sqrt{3}=0\) and \(x+\sqrt{2} y+2-\sqrt{3}=0\) is
\(\frac{|2+\sqrt{3}-2+\sqrt{3}|}{\sqrt{1+2}}=\frac{2 \sqrt{3}}{\sqrt{3}}=2 \text { units. }\)
Hence, option (b) is correct.