TS EAMCET · Maths · Application of Derivatives
For the curve \(\frac{x^n}{a^n}+\frac{y^n}{b^n}=2,(n \in \mathbb{N} ~\&~ n>1)\) the line \(\frac{x}{a}+\frac{y}{b}=2\) is
- A a normal for all values of \(n\)
- B a normal for only values of \(n\) more than \(\operatorname{Max}\{a, b\}\)
- C a tangent for all values of \(n\)
- D a tangent for only values of \(n\) more than \(\operatorname{Min}\{a, b\}\)
Answer & Solution
Correct Answer
(C) a tangent for all values of \(n\)
Step-by-step Solution
Detailed explanation
At \( (x,y)=(a,b) \): Curve: \( \frac{a^n}{a^n}+\frac{b^n}{b^n}=1+1=2 \). Line: \( \frac{a}{a}+\frac{b}{b}=1+1=2 \). Implicit differentiation of curve: \( \frac{n x^{n-1}}{a^n} + \frac{n y^{n-1}}{b^n} \frac{dy}{dx} = 0 \). Slope of tangent at \( (a,b) \):…
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