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AP EAMCET · Maths · Application of Derivatives

The angle between the curves \(y^2=2 x\) and \(x^2+y^2=8\) is

  1. A \(\tan ^{-1}(1)\)
  2. B \(\tan ^{-1}(2)\)
  3. C \(\tan ^{-1}(3)\)
  4. D \(\tan ^{-1}\left(-\frac{1}{2}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\tan ^{-1}(3)\)

Step-by-step Solution

Detailed explanation

\(y^2=2 x\) and \(x^2+y^2=8\) Solving, \(x^2+2 x-8=0 \Rightarrow(x+4)(x-2)=0\) \(x=2 \Rightarrow y=2 \quad[\because x \neq-4]\) \(2 y y_1^{\prime}=2 \quad y_1^{\prime}=\frac{1}{2} \Rightarrow x+y y_2^{\prime}=0 \Rightarrow y_2^{\prime}=-\frac{x}{y}=-1\)…