Q. The length of the perpendicular from the origin of the line $\frac{x\sin\alpha}{b} - \frac{y\cos\alpha}{a} - 1 = 0\ is$
A) $\frac{|ab|}{\sqrt{a^{2}\cos^{2}\alpha - b^{2}\sin^{2}\alpha}}$
B) $\frac{|ab|}{\sqrt{a^{2}\cos^{2}\alpha + b^{2}\sin^{2}\alpha}}$
C) $\frac{|ab|}{\sqrt{a^{2}\sin^{2}\alpha - b^{2}\cos^{2}\alpha}}$
D) $\frac{|ab|}{\sqrt{a^{2}\sin^{2}\alpha + b^{2}\cos^{2}\alpha}}$
Explanation
(d)
The length of perpendicular from the origin to the line
$\frac{x\sin\alpha}{b} - \frac{y\cos\alpha}{a} - 1 = 0\ is$
$d = \frac{|0 - 0 - 1|}{\sqrt{\frac{\sin^{2}\alpha}{b^{2}} + \frac{\cos^{2}\alpha}{a^{2}}}}$
$= \frac{|ab|}{\sqrt{a^{2}\sin^{2}\alpha + b^{2}\cos^{2}\alpha}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.