Find the equation of the straight line on which the length of the perp

1.	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 = \(\frac{1}{3}\) .
Answer» Given: p = 2, sinα = 1/3 We know that, cos α = \(\sqrt{1-sin^2α}\) ⇒ \(\sqrt{1-\frac{1}{9}}\) = \(\frac{2\sqrt{2}}{3}\) Concept Used: The equation of a line in normal form. Explanation: So, the equation of the line in normal form is Formula Used: x cos α + y sin α = p ⇒ \(\frac{2\sqrt{2}}{3}x+\frac{y}{3}=2\) ⇒ 2√2x + y = 6 Hence, the equation of line in normal form is 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 sin α = \(\frac{1}{3}\) .

Answer»

Given: p = 2, sinα = 1/3

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

⇒ \(\sqrt{1-\frac{1}{9}}\) = \(\frac{2\sqrt{2}}{3}\)

Concept Used:

The equation of a line in normal form.

Explanation:

So, the equation of the line in normal form is

Formula Used: x cos α + y sin α = p

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

⇒ 2√2x + y = 6

Hence, the equation of line in normal form is 2√2x + y = 6