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Intersection of f(x,y)=x² + y² and g(x,y) = xy+2

Intersection of f(x,y)=x² + y² and g(x,y) = xy+2
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2018-07-10 18:41
FunctionCoordinate GeometryTransformation
In collections intersection: surface-surface, curve-curve
This example demonstrates finding the intersection points of two functions in the Cartesian plane. Key mathematical concepts include functions and coordinate geometry. It utilizes commands like Point and CurveCartesian in GeoGebra for construction. Suitable for high school students or those learning coordinate geometry.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. FirstAxis(c) → h
  3. Angle(xAxis, h) → α
  4. Rotate(c, (-α)) → c'
  5. CurveCartesian((2 * sin(t)), (2 * cos(t) / sqrt(3)), t, 0, (2 * π)) → b
  6. Rotate(b, α) → b'
  7. CurveCartesian((2 / sqrt(2) * (sin(t) - cos(t) / sqrt(3))), (2 / sqrt(2) * (sin(t) + cos(t) / sqrt(3))), f((2 / sqrt(2) * (sin(t) - cos(t) / sqrt(3))), (2 / sqrt(2) * (sin(t) + cos(t) / sqrt(3)))), t, 0, (2 * π)) → e