Q. If the line $y\cos\alpha\text{=}x\sin\alpha + a\cos\alpha$ be a tangent to the circle $x^{2} + y^{2} = a^{2}$, then
A) $\sin^{2}\alpha = 1$
B) $\cos^{2}\alpha = 1$
C) $\sin^{2}\alpha = a^{2}$
D) $\cos^{2}\alpha = a^{2}$
Explanation
(b)
Given, $y = a\tan\alpha + a$
Condition for tangency is $a^{2} = a^{2}(1 + \tan^{2}\alpha)$
$\lbrack\because\ \ c^{2} = a^{2}(1 + m^{2})\rbrack$
$\Rightarrow \ \ \sec^{2}\alpha = 1$
$\Rightarrow \ \ \cos^{2}\alpha = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.