Parabola

a plane curve traced out by a point moving so that its distance from a fixed point (focus) is equal to its perpendicular distance from a fixed straight line (directrix). It is also the curve made by cutting a cone with a flat plane that is parallel to the side of the cone that slopes. Mirrors with a parabolic shape are used in searchlights and telescopes because incoming parallel rays of light are reflectd onto the focus. This property is used in a telescope, and thus the reverse applies in searchlights.

Taken from Dictionary of Science

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In mathematics, the parabola (pronounced /pəˈræbələ/, from the Greek παραβολή) is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. Given a point (the focus) and a corresponding line (the directrix) on the plane, the locus of points in that plane that are equidistant from them is a parabola.

The parabola has many important applications, from automobile headlight reflectors to the design of ballistic missiles. They are frequently used in physics, engineering, and many other areas.

Taken from Wikipedia

Tangent

a function of an angle in a right-angled triangle, defined as the ratio of the side opposite the angle to the length of the side adjacent to it. Also, in geometry, a straight line that just touches the circumference of a circle.

Taken from Dictionary of Science

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In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that "just touches" the curve at that point (in the sense explained more precisely below). As it passes through the point of tangency, the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point. The same definition applies to space curves and curves in n-dimensional Euclidean space.

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, meaning "to touch".

Taken from Wikipedia