If at any point on a curve the subtangent and subnormal are equal, then the tangent is equal to

ordinate $\sqrt{2}$ ordinate $\sqrt{2 \text { (ordinate) }}$ none of these

$\sqrt{2}$ ordinate

We have, Subtangent = Subnormal $\Rightarrow \frac{y}{\frac{d y}{d x}}=y \frac{d y}{d x} \Rightarrow \frac{d y}{d x}= \pm 1$ ∴   Length of the tangent = $\frac{y \sqrt{1+\left(\frac{d y}{d x}\right)^2}}{\frac{d y}{d x}}=y \sqrt{2}=\sqrt{2} y$