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Question
Find the equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle α with x-axis such that sin α = \[\frac{1}{3}\].
Solution
Here, p = 2,
\[\text { sin }\alpha = \frac{1}{3}\]
\[\therefore \text { cos}\alpha = \sqrt{1 - \sin^2 \alpha}\]
\[ \Rightarrow\text { cos }\alpha = \sqrt{1 - \frac{1}{9}} = \frac{2\sqrt{2}}{3}\]
So, the equation of the line in normal form is
\[x\text { cos }\alpha + y\text { sin }\alpha = p\]
\[ \Rightarrow \frac{2\sqrt{2}x}{3} + \frac{y}{3} = 2\]
\[ \Rightarrow 2\sqrt{2}x + y = 6\]
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