AP EAMCET · Maths · Application of Derivatives
An angle between the curves \(x^2=3 y\) and \(x^2+y^2=4\) is
- A \(\tan ^{-1} \frac{5}{\sqrt{3}}\)
- B \(\tan ^{-1} \sqrt{\frac{5}{3}}\)
- C \(\tan ^{-1} \frac{2}{\sqrt{3}}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\tan ^{-1} \frac{5}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Given curves are On solving Eqs. (i) and (ii), we get \[ \therefore \quad x= \pm \sqrt{3}, y=1 \] Thus, their points of intersection are \((\sqrt{3}, 1)\) and \((-\sqrt{3}, 1)\). Now, from Eq. (i), \(\frac{d y}{d x}=\frac{2 x}{3}\) and from Eq. (ii),…
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