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(C) Let the curve be $y = f(x)$. The length of the subtangent is given by $|y \frac{dx}{dy}|$ and the length of the subnormal is given by $|y \frac{dy

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$GP$

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(C) Let the curve be $y = f(x)$. The length of the subtangent is given by $|y \frac{dx}{dy}|$ and the length of the subnormal is given by $|y \frac{dy}{dx}|$. Let the ordinate be $y$. Then,the product of the subtangent and the subnormal is: $	ext{Subtangent} 	imes 	ext{Subnormal} = |y \frac{dx}{dy}| 	imes |y \frac{dy}{dx}| = |y^2| = y^2$. Since the product of the first and third terms equals the square of the second term (the ordinate),the three quantities form a Geometric Progression $(GP)$.

The length of the subtangent,ordinate,and the subnormal are in

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