If p and q are the lengths of perpendiculars from the origin to the lines x cos-y sin-3 cos 2 - and x -y cosec -3- respectively- then the value of p 2-4 q 2 isA- 4B- 6C- 5D- 9

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Byju's Answer

Standard XII

Physics

Introduction

If p and q ar...

Question

If p and q are the lengths of perpendiculars from the origin to the lines $x c o s θ - y s i n θ = 3 c o s 2 θ$ and $x s e c θ + y c o s e c θ = 3$ , respectively, then the value of $p^{2} + 4 q^{2}$ is

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Solution

The correct option is D
9

$P = ∣ ∣ ∣ \frac{- 3 c o s 2 θ}{\sqrt{s i n^{2} θ + c o s^{2} θ}} ∣ ∣ ∣ p = | 3 c o s 2 θ |$
and $q = ∣ ∣ ∣ \frac{3}{\sqrt{s e c^{2} θ + c o s e c^{2} θ}} ∣ ∣ ∣ = ∣ ∣ \frac{3 s i n 2 θ}{2} ∣ ∣ 2 q = | 3 s i n 2 θ | p^{2} + 4 q^{2} = 9$

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If p and q are the lengths of perpendicular from the origin to the lines $x c o s θ - y s i n θ = k c o s 2 θ$ and $x s e c θ + y c o s e c θ = k$ , respectively.

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If p and q are the length of perpendiculars from the origin to the lines $x c o s θ - y s i n θ = k c o s 2 θ$ and $x s e c θ + y c o s e c θ = k$ respectively, prove that $p^{2} + 4 q^{2} = k^{2}$