Intersect Command
From GeoGebra Manual
- Intersect[ <Object>, <Object> ]
- Yields the intersection points of two objects.
- Example:
- Let
a: -3x + 7y = -10
be a line with A = (1, -1) and B = (8, 2) andc: x^2 + 2y^2 = 8
be an ellipse with focuses C = (-2, 0) und D = (2, 0).Intersect[a, c]
yields the intersection points E = (-1.02, -1,87) and F = (2.81, -0.22) of the line and the ellipse. Intersect[y = x + 3, Curve[t, 2t, t, 0, 10]]
yields A(3,6).Intersect[Curve[2s, 5s, s,-10, 10 ], Curve[t,2t,t,-10,10]]
yields A(0,0).
- Let
- Intersect[ <Object>, <Object>, <Index of Intersection Point> ]
- Yields the nth intersection point of two objects.
- Example:Let
a(x) = x^3 + x^2 - x
be a function andb: -3x + 5y = 4
be a line with A = (-3, -1) and B = (2, 2).Intersect[a, b, 2]
yields the intersection point C = (-0.43, 0.54) of the function and the line.
- Intersect[ <Object>, <Object>, <Initial Point> ]
- Yields an intersection point of two objects by using a (numerical) iterative method with initial point.
- Example:Let
a(x) = x^3 + x^2 - x
be a function,b: -3x + 5y = 4
be a line with A = (-3, -1) and B = (2, 2) and C = (0, 0.8) be the initial point.Intersect[a, b, C]
yields the intersection point D = (-0.43, 0.54) of the function and the line by using a (numerical) iterative method.
- Intersect[ <Function>, <Function>, <Start x-Value>, <End x-Value> ]
- Yields the intersection points numerically for the two functions in the given interval.
- Example:Let
f(x) = x^3 + x^2 - x
andg(x) = 4 / 5 + 3 / 5 x
be two functions.Intersect[ f, g, -1, 2 ]
yields for the intervall [ -1, 2 ] the intersection points A = (-0.43, 0.54) and B = (1.1, 1.46) of the two functions.
- Intersect[ <Curve 1>, <Curve 2>, <Parameter 1>, <Parameter 2> ]
- Finds one intersection point using an iterative method starting at the given parameters.
- Example:Let
a = Curve[cos(t), sin(t), t, 0, π]
andb = Curve[cos(t) + 1, sin(t), t, 0, π]
.Intersect[a, b, 0, 2]
yields the intersection point A = (0.5, 0.87).
CAS Syntax
- Intersect[ <Function>, <Function> ]
- Yields the intersection points of two objects.
- Example:Let
f(x):= x^3 + x^2 - x
andg(x):= x
be two functions.Intersect[ f(x), g(x) ]
yields the intersection points {(1, 1), (0, 0), (-2, -2)} of the two functions.
Note: See also Intersect tool.
Following text is about a feature that is supported only in GeoGebra 5.0.
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