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​Q. PROVE THAT THE CONDITION FOR THE LINE Ax + By =1 TO BE NORMAL TO THE CURVE- a n-1 y = x n IS- ( nA ) n = B a n-1 ( nA 2 + B 2 ) n-1 .

​Q. PROVE THAT THE CONDITION FOR THE LINE Ax + By =1 TO BE NORMAL TO THE CURVE- an-1 y = xn IS-
 
( nA )n = Ban-1 ( nA2 + B2)n-1 .

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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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