Question

The product of the lengths of subtangent and subnormal at any point $ (x,\text{ }y) $ of a curve is:

• A. $ {{x}^{2}} $
• B. $ {{y}^{2}} $
• C. a constant
• D. $ x $
• E. $ y $

Answer 1

Answer: (B)

$ \because $ Length of sub tangent $ =\frac{y}{\left( \frac{dy}{dx} \right)} $ and length of subnormal $ =y\frac{dy}{dx} $ $ \therefore $ Product of subtangent and subnormal $ =\frac{y}{\left( \frac{dy}{dx} \right)}.y\frac{dy}{dx}={{y}^{2}} $