Question

If the distance between the parallel lines given by the equation $x^{2}+4xy+py^{2}+3x+qy-4=0$ is $\lambda$, then $\lambda^{2}=$

• A. 5
• B. $\sqrt{5}$
• C. 25
• D. $\frac{9}{5}$

Hint:

Logic Tip: The distance between parallel lines given by the general 2nd degree equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ can be found directly using the formula $d = 2\sqrt{\frac{g^2-ac}{a(a+b)$. Here $a=1, b=4, c=-4, g=3/2$. So $d = 2\sqrt{\frac{9/4 - 1(-4)}{1(1+4) = 2\sqrt{\frac{25/4}{5 = 2\sqrt{5/4} = \sqrt{5}$.

Answer 1

The Correct Option is A