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Differential Calculus> Q. PROVE THAT THE CONDITION FOR THE LINE...

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Q. PROVE THAT THE CONDITION FOR THE LINE Ax + By =1 TO BE NORMAL TO THE CURVE- a^n-1y = xⁿ IS-

( nA )ⁿ = Ba^n-1 ( nA² + B²)^n-1.

Bharat Makkar , 10 Years ago

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1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$a^{n-1}y = x^n$
$a^{n-1}y' = nx^{n-1}$
Slope of normal:
$\frac{-1}{y'} = \frac{-a^{n-1}}{nx^{n-1}}$
Slope of line: -A/B
$\frac{-A}{B} = \frac{-a^{n-1}}{nx^{n-1}}$
$\frac{A}{B} = \frac{a^{n-1}}{nx^{n-1}}$
Condition is not written properly.
But you can proceed from here by manipulating equation.

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