Question

Assertion (A): The distance between the lines represented by $x^2+2\sqrt{2}xy+2y^2+4\sqrt{2}x+4y+1=0$ is 2
Reason (R): Distance between the lines $ax+by+c=0$ and $ax+by+c_1=0$ is $\frac{|c-c_1|}{\sqrt{(a^2+b^2)}}$

• A. Assertion is true.
• B. Reason is true.
• C. Both Assertion and Reason are true.
• D. Neither Assertion nor Reason are true.

Answer 1

The correct option is B Reason is true.

Reason is true
Assertion
$x^2+2\sqrt{2}xy+2y^2+4\sqrt{2}x+4y+1=0$ represents a pair of lines when $\Delta =0$
But $\Delta =\left|\begin{array}{ccc}1& \sqrt{2}& 2\sqrt{2}\\ \sqrt{2}& 4& 1\\ 2\sqrt{2}& 1& 1\end{array}\right|=-2$