For the curve "xⁿ/aⁿ + yⁿ/bⁿ = 2, (n {N} \ \& \ n > 1)" the line "x/a + y/b = 2" is

Correct Answer is : a tangent for all values of "n""n""n"

a normal for only values of "n" more than "\{a, b\}"

a tangent for all values of "n"

a tangent for only values of "n" more than "\{a, b\}"

Correct Answer is : a tangent for all values of "n""n""n"

Test Index

TG EAMCET 4 May 2025 Shift 2 Paper

Question : 67 of 160

Marks: +1, -0

For the curve

"\frac{x^n}{a^n} + \frac{y^n}{b^n} = 2, (n \in \mathbb{N} \ \& \ n > 1)"

"\frac{x}{a} + \frac{y}{b} = 2"

Solution:

Given,

"\frac{x^n}{a^n} + \frac{y^n}{b^n} = 2"

"\frac{1}{a^n} \times n \cdot x^{n-1} + \frac{n y^{n-1}}{b^n} \frac{dy}{dx} = 0"

"\frac{n y^{n-1}}{b^n} \frac{dy}{dx} = \frac{-1}{a^n} \times n \cdot x^{n-1}"

"\frac{dy}{dx} = \frac{-b^n}{a^n} \times \left( \frac{x}{y} \right)^{n-1}"

"\left( \frac{dy}{dx} \right)_{\alpha, \beta} = \frac{-b^n}{a^n} \times \left( \frac{\alpha}{\beta} \right)^{n-1} = \frac{-b}{a}"

Equation of tangent of

"(a, b)"

"y - b = \frac{-b}{a} (x - a)"

"a y - a b = -b x + a b"

"b x + a y = 2 a b \Rightarrow \frac{x}{a} + \frac{y}{b} = 2"

∴ Tangent for all value of

"n"

Go to Question:

Prev Question

Next Question