The length of the perpendicular from the poin | vedclass

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(C) The given equation of the line is $y = x 	an \alpha + c$,which can be rewritten as $x \sin \alpha - y \cos \alpha + c \cos \alpha = 0$.The length

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$c \cos \alpha$

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(C) The given equation of the line is $y = x 	an \alpha + c$,which can be rewritten as $x \sin \alpha - y \cos \alpha + c \cos \alpha = 0$.The length of the perpendicular $p$ from the point $(x_1, y_1) = (a \cos \alpha, a \sin \alpha)$ to the line $Ax + By + C = 0$ is given by $p = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$.Substituting the values:$p = \frac{|(a \cos \alpha)(\sin \alpha) - (a \sin \alpha)(\cos \alpha) + c \cos \alpha|}{\sqrt{\sin^2 \alpha + \cos^2 \alpha}}$$p = \frac{|0 + c \cos \alpha|}{\sqrt{1}}$Since $c > 0$ and assuming $\cos \alpha > 0$,we get $p = c \cos \alpha$.

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

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