If at any point on a curve the subtangent and subnormal are equal, then the tangent is equal to
Answer & explanation
Correct answer: option 2
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 = $\frac{y \sqrt{1+\left(\frac{d y}{d x}\right)^2}}{\frac{d y}{d x}}=y \sqrt{2}=\sqrt{2} y$