Question

Distance between two lines respresented by the line pair, $x^2-4xy+4y^2+x-2y-6=0$ is

• A. $\frac{1}{\sqrt{5}}$
• B. $\sqrt{5}$
• C. $2\sqrt{5}$
• D. none of these

Answer 1

The correct option is B $\sqrt{5}$

As $h^2=4=1\times 4=ab$ and $b{g}^2=4\times \left(\frac{1}{4}\right)=1\times \left(1\right)=a{f}^2$
Therefore the lines in $x^2-4xy+4y^2+x-2y-6=0$ are parallel
and the distance between the two lines
$=\frac{2\sqrt{g^2-ac}}{\sqrt{a(a+b)}}=\frac{2\sqrt{\frac{1}{4}-1\times (-6)}}{\sqrt{1(1+4)}}=\frac{\sqrt{25}}{\sqrt{5}}=\sqrt{5}$