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 $s i n α = \frac{1}{3} .$

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Solution

$Here p = 2, s i n α = \frac{1}{3}$

$\Rightarrow c o s α = \frac{2 \sqrt{2}}{3}$

$The equation of straight line is$

$x c o s α + y s i n α = p$

$x (\frac{2 \sqrt{2}}{3}) + y (\frac{1}{3}) = 2$

$2 \sqrt{2} x + y = 6$

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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=13.

Here p=2, sin α=13 ⇒ cos α=2√23 The equation of straight line is x cos α+y sin α=p x(2√23)+y(13)=2 2√2x+y=6

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 $s i n α = \frac{1}{3} .$

$Here p = 2, s i n α = \frac{1}{3}$

$\Rightarrow c o s α = \frac{2 \sqrt{2}}{3}$

$The equation of straight line is$

$x c o s α + y s i n α = p$

$x (\frac{2 \sqrt{2}}{3}) + y (\frac{1}{3}) = 2$

$2 \sqrt{2} x + y = 6$