In geometry, the **tangent line** (or simply the **tangent**) to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve *y* = *f*(*x*) at a point *x* = *c* on the curve if the line passes through the point (*c*, *f*(*c*)) on the curve and has slope *f*'(*c*) where *f*' is the derivative of *f*. A similar definition applies to space curves and curves in *n*-dimensional Euclidean space.

As it passes through the point where the tangent line and the curve meet, called the *point of tangency*, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point.

Similarly, the **tangent plane** to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space.

The word *tangent* comes from the Latin *tangere*, *to touch*.

Read more about Tangent: History, Tangent Line To A Curve, Tangent Circles, Surfaces and Higher-dimensional Manifolds

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