COMEDK · Maths · 27. Application of Derivatives
For the curve \(y^{n}=a^{n-1} x\) if the subnormal at any point is a constant, then \(n\) is equal to
- A \(1\)
- B \(2\)
- C \(-2\)
- D \(-1\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
We have, \(y^{n}=a^{n-1} x\) \(\Rightarrow \quad n \cdot y^{n-1} \frac{d y}{d x}=a^{n-1}\) \(\Rightarrow \quad y^{n-1} \frac{d y}{d x}=\frac{1}{n} a^{n-1}\) \(\Rightarrow \quad \frac{d y}{d x}=\frac{1}{n} a^{n-1} y^{1-n}\) \(\therefore \quad\) Length of the subnormal…
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