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Q.

For the curve $y^{2} = x^{2}$ at (4, 8) A,B,C,D denotes the length of tangent, Sub tangent, Normal, Sub normal respectively then the decreasing order is

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a

B, D, A, C

b

C, D, B, A

c

C, D, A, B

d

D, C, B, A

answer is D.

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Detailed Solution

$\begin{array}{rcl} y^{2} & = & x^{3} \Rightarrow 2 y \frac{dy}{dx} = 3 x^{2} \\ \Rightarrow & \frac{dy}{dx} = \frac{3 \times 16}{2 \times 8} = 3 \\ A & = & L . T = |8 \frac{\sqrt{1 + 9}}{3}| = \frac{8 \sqrt{10}}{3} \\ B & = & L . S . T = \frac{8}{3} \\ C & = & L . S . T = 8 \sqrt{10} \\ D & = & 8 \times 3 = 24 \end{array}$

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