Question

At any point of a curve $\sqrt{\frac{subnormal}{subtangent}}$ is equal to -

• A. the abscissa of that point
• B. the ordinate of that point
• C. slope of the tangent at that point
• D. slope of the normal at that point

Answer 1

The correct option is C slope of the tangent at that point

We know, $\text{subnormal}=y\frac{dy}{dx}$
and $\text{subtangent}=\frac{y}{\frac{dy}{dx}}$
Therefore, $\sqrt{\frac{\text{subnormal}}{\text{subtangent}}}=\frac{dy}{dx}=$ slope of tangent to the curve ${}^{\prime }{y}^{\prime }$ at any point.
Hence, option 'C' is correct.