For any point on a curve,what is sqrt{frac{te | vedclass

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(C) Let the slope of the tangent at a point $(x, y)$ on the curve be $m = \frac{dy}{dx}$.The length of the subtangent is given by $|\frac{y}{m}| = |y

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Slope of the tangent at the point

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(C) Let the slope of the tangent at a point $(x, y)$ on the curve be $m = \frac{dy}{dx}$.The length of the subtangent is given by $|\frac{y}{m}| = |y \frac{dx}{dy}|$.The length of the subnormal is given by $|my| = |y \frac{dy}{dx}|$.Now,consider the expression $\sqrt{\frac{	ext{subnormal}}{	ext{subtangent}}}$.Substituting the formulas,we get $\sqrt{\frac{|y \frac{dy}{dx}|}{|y \frac{dx}{dy}|}} = \sqrt{|\frac{dy}{dx} \cdot \frac{dy}{dx}|} = \sqrt{(\frac{dy}{dx})^2} = |\frac{dy}{dx}|$.Thus,$\sqrt{\frac{	ext{subnormal}}{	ext{subtangent}}} = |\frac{dy}{dx}|$,which is the magnitude of the slope of the tangent at that point.

For any point on a curve,what is $\sqrt{\frac{\text{subnormal}}{\text{subtangent}}}$ equal to?

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