TS EAMCET · Maths · Differentiation
If \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), then \(\frac{d^2 y}{d x^2}=\)
- A \(-\frac{b^4}{a^2 y^3}\)
- B \(\frac{b^2}{a y^2}\)
- C \(\frac{-b^3}{a^2 y^3}\)
- D \(\frac{b^3}{a^2 y^2}\)
Answer & Solution
Correct Answer
(A) \(-\frac{b^4}{a^2 y^3}\)
Step-by-step Solution
Detailed explanation
We have, \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] Let \(x=a \cos \theta, y=b \sin \theta\) \[ \begin{aligned} \therefore \quad \frac{d x}{d \theta} & =-a \sin \theta, \frac{d y}{d \theta}=b \cos \theta \\ \frac{d y}{d x} & =-\frac{b}{a} \cot \theta \end{aligned} \] On…
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