AP EAMCET · Maths · Application of Derivatives
The length of the tangent drawn at the point \(p\left(\frac{\pi}{4}\right)\) on the curve \(x^{\frac{2}{3}}+y^{\frac{2}{3}}=2^{\frac{2}{3}}\) is
- A \(\frac{2}{3}\)
- B \(1\)
- C \(\frac{4}{3}\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
Given the curve \(x^{\frac{2}{3}}+y^{\frac{2}{3}}=2^{\frac{2}{3}}\) Let \(x=2 \cos ^3 \theta, y=2 \sin ^3 \theta\) Now, \(\frac{d y}{d x}=-\tan \theta\) at \(\theta=\frac{\pi}{4}, \frac{d y}{d x}=-1\) and \(x=\frac{2}{2 \sqrt{2}}=\frac{1}{\sqrt{2}}\) and,…
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