Tangent Command

Tangent( <Point>, <Conic> )

Creates (all) tangents through the point to the conic section.

Example:

Tangent[(5, 4), 4x^2 - 5y^2 = 20] yields x - y = 1.

Tangent( <Point>, <Function> )

Creates the tangent to the function at x = x(A).

Note: x(A) is the x-coordinate of the given point A.

Example:

Tangent[(1, 0), x^2] yields y = 2x - 1.

Tangent( <Point on Curve>, <Curve> )

Creates the tangent to the curve in the given point.

Example:

Tangent[(0, 1), Curve[cos(t), sin(t), t, 0, π]] yields y = 1.

Tangent( <x-Value>, <Function> )

Creates the tangent to the function at x-Value.

Example:

Tangent[1, x^2] yields y = 2x - 1.

Tangent( <Line>, <Conic> )

Creates (all) tangents to the conic section that are parallel to the given line.

Example:

Tangent[y = 4, x^2 + y^2 = 4] yields y = 2 and y = -2.

Tangent( <Circle>, <Circle> )

Creates the common tangents to the two Circles (up to 4).

Example:

Tangent[x^2 + y^2 = 4, (x - 6)^2 + y^2 = 4] yields y = 2, y = -2, 1.49x + 1.67y = 4.47 and -1.49x + 1.67y = -4.47.

Tangent( <Point>, <Spline> )

Creates the tangent to the spline in the given point.

Example:

Let A = (0, 1), B = (4, 4) and C = (0, 4).

Tangent[A, Spline[{A, B, C}]] yields line a: y = 0.59x + 1.

Note: See also Tangents tool.