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AP EAMCET · Maths · Straight Lines

The equation of the line, passing through the point \(\left(a \cos ^3 \theta, a \sin ^3 \theta\right)\) and perpendicular to the line \(x \cos\) \(\theta-y \sin \theta=a\), is

  1. A \(2 x \sin \theta+2 y \cos \theta=a \sin 2 \theta\)
  2. B \(x \cos \theta-y \sin \theta=a \sin 2 \theta\)
  3. C \(x \sin \theta+y \sin \theta=a \cos 2 \theta\)
  4. D \(x \sin \theta-y \cos \theta=a \cos 2 \theta\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2 x \sin \theta+2 y \cos \theta=a \sin 2 \theta\)

Step-by-step Solution

Detailed explanation

Slope of line \(\mathrm{x} \cos \theta-\mathrm{y} \sin \theta=\mathrm{a}\) is \(\mathrm{m}^{\prime}=\cot \theta\) So, the slope of the required line is: \(m=\frac{-1}{m^{\prime}}=-\tan \theta\) Now, the required equation of line is:…