TS EAMCET · Maths · Application of Derivatives
An angle between the curves \(x^2-y^2=4\) and \(x^2+y^2\) \(=4 \sqrt{2}\) is
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(x^2-y^2=4\) ...(i) \(x^2+y^2=4 \sqrt{2}\) ...(ii) Adding both equations, \(\begin{aligned} & x^2=2(1+\sqrt{2}) \Rightarrow x=\sqrt{2} \sqrt{\sqrt{2}+1} \\ & \therefore \quad y^2=2(\sqrt{2}-1) \Rightarrow y=\sqrt{2} \sqrt{\sqrt{2}-1}\end{aligned}\) Differentiating both (i) and…
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