The length of perpendicular from the point $(a\cos\alpha,\ a\sin\alpha)$ upon the straight line $y = x an\alpha + c,\ c 0,$ is

Question

The length of perpendicular from the point $(a\cos\alpha,\ a\sin\alpha)$ upon the straight line $y = x	an\alpha + c,\ c > 0,$ is

Dr. Abubacker · Accepted Answer

(c)
The given line is $x	an\alpha - y + c = 0$
or $x\sin\alpha - y\cos\alpha + c\cos\alpha = 0$
$	herefore\$Length of perpendicular from $\left( a\cos\alpha,\ a\sin\alpha ight)$
$= \frac{a\cos\alpha\sin\alpha - a\ \sin\alpha\cos\alpha + c\cos\alpha}{\sqrt{\sin^{2}\alpha + \cos^{2}\alpha}}$
$= \frac{c\cos\alpha}{1} = c\cos\alpha$

Q. The length of perpendicular from the point $(a\cos\alpha,\ a\sin\alpha)$ upon the straight line $y = x\tan\alpha + c,\ c > 0,$ is

Explanation

Reviewed by Dr. Abubacker

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