AP EAMCET · Maths · Application of Derivatives
The length of the subnormal at any point on the curve \(y=\left(\frac{x}{2024}\right)^k\) is constant if the value of \(k\) is
- A 1
- B \(\frac{1}{3}\)
- C \(\frac{1}{2}\)
- D 0
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(y=\left(\frac{x}{2024}\right)^k\) Differentiating w.r.t. \(x\) \(\frac{d y}{d x}=\frac{k}{(2024)^k} x^{k-1}\) Length of subnormal is \(\left|y \frac{d y}{d x}\right|\) \(=\frac{k x^{2 k-1}}{(2024)^{2 k}}=\text { constant }\) \(\Rightarrow\) Independent of \(x\) and \(y\)…
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