AP EAMCET · Maths · Straight Lines
The line passing through \(\left(-1, \frac{\pi}{2}\right)\) and perpendicular to \(\sqrt{3} \sin \theta+2 \cos \theta=\frac{4}{r}\) is :
- A \(2=\sqrt{3} r \cos \theta-2 r \sin \theta\)
- B \(5=-2 \sqrt{3} r \sin \theta+4 r \cos \theta\)
- C \(2=\sqrt{3} r \cos \theta+2 r \sin \theta\)
- D \(5=2 \sqrt{3} r \sin \theta+4 r \cos \theta\)
Answer & Solution
Correct Answer
(A) \(2=\sqrt{3} r \cos \theta-2 r \sin \theta\)
Step-by-step Solution
Detailed explanation
Given, \(\sqrt{3} \sin \theta+2 \cos \theta=\frac{4}{r}\) ...(i) Any line perpendicular to Eq. (i) is \(\sqrt{3} \sin \left(\frac{\pi}{2}+\theta\right)+2 \cos \left(\frac{\pi}{2}+\theta\right)=\frac{k}{r}\) \(\sqrt{3} \cos \theta-2 \sin \theta=\frac{k}{r}\) It passes through…
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