Q. The equation ${8x}^{2} + 8xy + 2y^{2} + 26x + 13y + 15 = 0$ represents a pair of straight lines. The distance between then is
A) $\frac{7}{\sqrt{5}}$
B) $\frac{7}{2\sqrt{5}}$
C) $\frac{\sqrt{7}}{5}$
D) None of these
Explanation
(b)
Now, $h^{2} - ab = 4^{2} - 8(2) = 16 - 16 = 0$
The required distance between the parallel straight lines
$= 2\sqrt{\frac{169 - 120}{80}} = \frac{2 \times 7}{4\sqrt{5}} = \frac{7}{2\sqrt{5}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.