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  4. The length of the sub-tangent, ordinate and the sub-normal are in

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Q. The length of the sub-tangent, ordinate and the sub-normal are in

KCETKCET 2012Application of Derivatives

Solution:

$\because $ Subtangent $=y \times \frac{d x}{d y}$
and subnormal $=y \times \frac{d y}{d x}$
$\therefore $ Subtangent $\times$ subnormal $=y^{2}=(\text { ordinate })^{2}$
Hence, length of the subtangent, ordinate and the subnormal are in GP.