Hi

In simple terms , the tangent line gently touches the curve , while the normal line cuts through the curve at a right angle .

1 Tangent :

A tangent to a curve at a given point is a straight line that touches the curve at that point without crossing it . The tangent line has the same slope as the curve at the point of contact . It represents the instantaneous rate of change derivative of the curve at that point .

2 Normal :

A normal to a curve at a given point is a straight line that is perpendicular to the tangent at that point . It represents the direction in which the curve is not changing at the given point and it intersects the tangent at a right angle .

Thank you

Tangent:

A tangent is a straight line which touches the curve at only one point called the point of contact. Tangent is directed or perpendicular to the instantaneous direction of the curve at that point.

Normal:

A normal is a straight line perpendicular to the tangent at the point of contact. It passes through the point of contact and is perpendicular to the tangent at that point.

Applications:

Geometry: Tangents and normals are applied to get equations of lines that touch or meet curves at certain points.
Calculus: They can determine the derivative, which tells how quickly a function is changing at a given point.
Physics: They help describe the motion of objects, particularly in circular motion and projectile motion, using tangents and normals.
The notions of tangents and normals can solve a host of problems in geometry, calculus, and physics, if only understood.