TS EAMCET · Maths · Application of Derivatives
Let \(a\) be a fixed positive real number and \(n\) be an arbitrary constant. For the curve \(y=\frac{x^n}{a^{n-1}}\), if the length of the subnormal at any point \((\alpha, \beta)\) is proportional to \(a^2\), then \(n=\)
- A 2
- B 1
- C 0
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
We have, \(y=\frac{x^n}{a^{n-1}} \quad \therefore \frac{d y}{d x}=\frac{n x^{n-1}}{a^{n-1}}\) \(\therefore\) Length of subnormal \(=y \frac{d y}{d x}=\frac{x^n}{a^{n-1}} \times n \frac{x^{n-1}}{a^{n-1}}\) \(=n \frac{x^{2 n-1}}{a^{2 n-2}}\) \(\therefore\) Length of subnormal at…
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