TS EAMCET · Maths · Application of Derivatives
If \(\theta\) is the angle between the curves \(x^2-y^2=4\) and \(y^2=3 x\) then \(\tan \theta=\)
- A \(\frac{5}{3 \sqrt{3}}\)
- B \(\frac{5}{6 \sqrt{3}}\)
- C \(\frac{5}{18}\)
- D \(\frac{5}{6}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{6 \sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Given curves are \(x^2-y^2=4\) and \(y^2=3 x\) on solving curves we get \(\mathrm{x}=4\) and \(\mathrm{y}=\sqrt{3}\) Now \(\tan \theta=\left|\frac{\frac{4}{\sqrt{3}}-\frac{3}{2 \sqrt{3}}}{1+\frac{4}{\sqrt{3}} \times \frac{3}{2 \sqrt{3}}}\right|=\frac{5}{6 \sqrt{3}}\)
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