For a curve $\frac{\text { (length of normal) }}{\text { (length of tangent) }}$ is equal to

subtangent subnormal slope of tangent slope of normal

slope of tangent

We have, Length of normal $=y \sqrt{1+\left(\frac{d y}{d x}\right)^2}$ Length of tangent $=\frac{y \sqrt{1+\left(\frac{d y}{d x}\right)^2}}{\frac{d y}{d x}}$ ∴  $\frac{\text { Length of normal }}{\text { Length of tangent }}=\frac{d y}{d x}=$ Slope of tangent