# Tangent Command ##### Command Categories (All commands)

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.
Tangent( <Point>, <Implicit Curve> )
Creates the tangent to the implicit curve in the given point.
Example: `Tangent((1,1), x^2+y^2=1))` yields lines x=1 and y=1.

Note: See also Tangents tool.
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