Question

What is tangent line and normal line?

Answer 1

Tangent line: The line that touches the curve at exactly one point and has the same slope as the curve at that point is called the tangent line.

Tangent of a line $y=mx+c$at a point $\left(a,b\right)$ is $y-b={\left[\frac{dy}{dx}\right]}_{\left(a,b\right)}\left(x-a\right)$.

Normal line: The line which is perpendicular to the tangent line is called the normal line.

Normal of a line $y=mx+c$at a point $\left(a,b\right)$ is $y-b=-{\left[\frac{dx}{dy}\right]}_{\left(a,b\right)}\left(x-a\right)$.