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Q.

If the tangent at any point $(4 m^{2}, 8 m^{3})$ of $x^{3} - y^{2} = 0$ is a normal to the curve $x^{3} - y^{2} = 0$ then value of m are

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a

$\pm \frac{1}{3}$

b

$\pm \sqrt{\frac{9}{2}}$

c

$\pm \sqrt{\frac{2}{9}}$

d

$\pm \frac{2}{3}$

answer is A.

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Detailed Solution

$y^{2} = x^{3} a n d \frac{d y}{d x} = \frac{3 x^{2}}{2 y}$

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