TS EAMCET · Maths · Application of Derivatives
If the tangent and normal drawn to the curve \(x=a(\theta+\sin \theta), y=a(1-\cos \theta)\) at \(P\left(\theta=\frac{\pi}{2}\right)\) cuts the \(\mathrm{X}\)-axis at \(A\) and \(B\) respectively, then the area (in sq. units) of \(\triangle P A B\) is
- A \(\frac{a^2}{\sqrt{2}}\)
- B \(\frac{\sqrt{2}}{a^2}\)
- C \(a^2\)
- D \(2 a^2\)
Answer & Solution
Correct Answer
(C) \(a^2\)
Step-by-step Solution
Detailed explanation
Given curve is \(x=a(\theta+\sin \theta), y=a(1-\cos \theta)\) \(\therefore \quad \frac{d y}{d x}=\frac{\sin \theta}{1+\cos \theta}=\tan \frac{\theta}{2}\) \(\therefore\) Slope of tangent and normal drawn to the given curve at \(P\left(\theta=\frac{\pi}{2}\right)\) is \(m_T=1\)…
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