What is meant by 'tangent to the path?

Answer 1

The immediate surroundings of any point on a curved path can be considered as part of a circle: the circle of curvature at that point. Then the tangent to the path at that point is a line that meets the path at only one point in that neighbourhood and which is perpendicular to the line joining the point to the centre of the circle or curvature.

The concept can be extended to straight segments of the path by assuming that the centre of curvature is at an infinite distance. In that case, the path and its tangent are the same line.

Answer 2

In mathematics, a tangent to a path refers to a line that touches the path at a single point without crossing through it. It represents the instantaneous direction of motion at that point on the path. Tangents are often used in calculus to calculate rates of change or slopes of curves at specific points. In physics, tangents to the path of a moving object can represent its velocity or acceleration at a given moment.

Answer 3

The tangent to a curve at a point refers to the straight line that best approaches the curve. In other words, in a small interval the straight line it will go in the same direction as the curve.