For a curve $\frac{(\text { Length of normal })^2}{(\text { Length of tangent })^2}$ is equal to

(subnormal) / (subtangent) (subtangent) / (subnormal) (tangent) / (normal) constant

(subnormal) / (subtangent)

We have, $\frac{(\text { Length of normal })^2}{(\text { Length of tangent })^2}=\left(\frac{d y}{d x}\right)^2$ $\Rightarrow \frac{(\text { Length of normal })^2}{(\text { Length of tangent })^2}=\frac{\text { Sub normal }}{\text { Sub tangent }}$