Perpendicular distance from the origin is 5 ...

NCERT Class XI Mathematics - Straight Lines - Solutions

Question : 22 of 74

Marks: +1, -0

Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30°.

Solution:

Here, we are given that p = 5 and ω = 30°.

cos 30° =

\frac{\sqrt{3}}{2}

and sin 30° =

\frac{1}{2}

By normal form, equation of the line is

x cos ω + y sin ω = p

⇒

\frac{\sqrt{3}}{2}x + \frac{1}{2}y

= 5 ⇒

\sqrt{3}x + y

= 10

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