AP EAMCET · Maths · Application of Derivatives
If the subnormal at any point on the curve \(y^n=a x\) is constant then the value of \(n\) is
- A 1
- B 2
- C 3
- D 0
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Equation of given curve \(y^n=a x\), so \(n y^{n-1} \frac{d y}{d x}=a \Rightarrow \frac{d y}{d x}=\frac{a}{n} y^{1-n}\) \(\therefore\) The length of subnormal \(=\left|y \frac{d y}{d x}\right|=\left|y \frac{a}{n} y^{1-n}\right|\) \(=\left|\frac{a}{n} y^{2-n}\right|\) It is given…
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