AP EAMCET202018 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

If the subnormal at any point on the curve (y^n=a x ) is constant then the value of (n ) is

Options

Correct answer

B. 2

Step-by-step solution

Equation of given curve (y^n=a x ), so (n y^ n-1 d y d x =a d y d x = a n y^ 1-n ) ( ) The length of subnormal (= |y d y d x |= |y a n y^ 1-n | ) (= | a n y^ 2-n | ) It is given that length of subnormal is constant, means it must be independent of (x ) and (y ) terms, so (n=2 ). Hence, option (b) is correct.

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