For a curve $\frac{\text { (length of normal) }}{\text { (length of tangent) }}$ is equal to
Answer & explanation
Correct answer: option 3
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