Q. The distance between the pair of parallel lines $x^{2} + 2xy + y^{2} - 8ax - 8ay - 9a^{2} = 0$ is
A) $2\sqrt{5}a$
B) $\sqrt{10}a$
C) $10\ a$
D) $5\sqrt{2}a$
Explanation
(d)
Here $a = 1,\ h = 1,\ f = - 4a,\ \ g = - 4a,\ c = - 9a$
Now, required distance
$= \left| 2\sqrt{\frac{f^{2} - bc}{b(b + a)}} \right|$
$= \left| 2\sqrt{\frac{16a^{2} + {9a}^{2}}{1(1 + 1)}} \right|$
$= \left| 2\sqrt{\frac{25a^{2}}{2}} \right| = \frac{5a}{\sqrt{2}} \bullet 2$
$= 5\sqrt{2}a$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.