Tangent Command
From GeoGebra Manual
- 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.