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AP EAMCET201923 Apr 2019Morning ShiftMathematicsApplication of DerivativesActual

If (T ) is the length of the subtangent drawn at any point on the curve (3 y^2=4 x^3 ) and (N ) is the length of the subnormal at the same point, then (( T)^2= )

Options

  1. A(4 N^2 )
  2. B(4 ~N )
  3. C(2 ~N )
  4. D(8 ~N ^2 )

Correct answer

C. (2 ~N )

Step-by-step solution

The equation of given curve is (3 y^2=4 x^3 ) ...(i) Let a point (P(h, k) ) on the curve (i), so ( . d y d x |_ (h, k) = 2 h^2 k ) Now, length of sub-tangent, (T= |k k 2 h^2 |= 1 2 k^2 h^2 ) and length of sub-normal, (N= |k 2 h^2 k |=2 h^2 ) ( (3 T)^2= 9 4 k^4 h^4 = 16 h^6 4 h^4 =4 h^2=2 N ) Hence, option (c) is correct.

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