Q. The distance between the pair of lines represented by the equation $x^{2} - 6xy + 9y^{2} + 3x - 9y - 4 = 0$ is
A) $\frac{15}{\sqrt{10}}$
B) $\frac{1}{2}$
C) $\sqrt{\frac{5}{2}}$
D) $\frac{1}{\sqrt{10}}$
Explanation
(c)
$Here,\ a = 1,\ \ h = - 3,\ \ b = 9,\ \ g = \frac{3}{2},\ \ f = - \frac{9}{2}\ and\ c = - 4$
$\therefore Required\ distance = \left| 2\sqrt{\frac{f^{2} - bc}{b(a + b)}} \right|$
$= \left| 2\sqrt{\frac{\left( - \frac{9}{2} \right)^{2} + (9)(4)}{9(9 + 1)}} \right|$
$= \left| 2\sqrt{\frac{225}{4 \times 90}} \right| = \left| \frac{2\sqrt{5}}{2\sqrt{2}} \right| = \sqrt{\frac{5}{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.