TS EAMCET · Maths · Application of Derivatives
If \(\theta\) is the acute angle between the curves \(x^2+y^2=4\) and \(y^2=3 x\) then \(\tan \theta=\)
- A \(\frac{5}{\sqrt{3}}\)
- B \(\frac{\sqrt{3}}{4}\)
- C \(\frac{4}{\sqrt{3}}\)
- D \(\frac{\sqrt{3}}{5}\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Given curves are \(x^2+y^2=4\) and \(y^2=3 x\) Put the value of \(y^2\). \[ \begin{aligned} & \Rightarrow x^2+3 x-4=0 \\ & \Rightarrow x^2+4 x-x-4=0 \\ & x(x+4)-1(x+4)=0 \\ & (x-1)(x+4)=0 \\ & x-1=0, x+4=0 \\ & x=1, x=-4 \end{aligned} \] Put in \(y^2=3 \mathrm{x}\), then,…
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