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 =$$\dfrac{1}{3}$$

Asked by Aaryan | 1 year ago |  53

##### Solution :-

Given:

p = 2, sin α = $$\dfrac{1}{3}$$

We know that cos α = $$\sqrt{(1 – sin^2 α)}$$

= $$\sqrt{(1 – \dfrac{1}{9}})$$

= $$\dfrac{2\sqrt{2}}{3}$$

The equation of the line in normal form is given by

By using the formula,

x cos α + y sin α = p

Now, substitute the values, we get

$$\dfrac{x^2\sqrt{2}}{3}+\dfrac{y}{3}=2$$

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

The equation of line in normal form is $$2\sqrt{2}x + y = 6$$

Answered by Aaryan | 1 year ago

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