TS EAMCET · Maths · Application of Derivatives
The tangent of the angle between the curves \(x y=1\) and \(x^2+8 y=0\), is
- A \(\frac{1}{7}\)
- B \(\frac{2}{7}\)
- C \(\frac{6}{7}\)
- D \(\frac{3}{7}\)
Answer & Solution
Correct Answer
(C) \(\frac{6}{7}\)
Step-by-step Solution
Detailed explanation
We have, \[ x y=1 \] and \(x^2+8 y=0\) On solving Eqs. (i) and (ii), we get \[ x=-2, y=-\frac{1}{2} \] Now, \(x y=1\) \[ \Rightarrow \frac{d y}{d x}=-\frac{y}{x} \Rightarrow\left(\frac{d y}{d x}\right)_{\left(-2, \frac{-1}{2}\right)}=-\frac{1}{4}=m_1 \] and…
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