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Intersection Curve of Two Quadrics

Intersection Curve of Two Quadrics
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2016-08-29 19:35
Coordinate GeometrySolid GeometryGeometric Construction
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the intersection curve of two quadrics. Key mathematical concepts include quadrics, coordinate geometry, and locus. Using GeoGebra commands Sequence and If, the intersection curve can be constructed. Suitable for high school mathematics education and students learning coordinate geometry.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[CurveCartesian[t, (i * sqrt((4 - t^(2)) / d)), (j * sqrt(t^(2) / b + (a / ((d * b)) * (4 - t^(2))) - c / b)), t, tmin, tmax], i, -1, 1, 2], j, -1, 1, 2) → l1
  2. Sequence(Sequence[CurveCartesian[(i * 2), t, (j * sqrt((4 + (a * t^(2)) - c) / b)), t, tmin, tmax], i, -1, 1, 2], j, -1, 1, 2) → l2
  3. If(d ≟ 0, l2, l1) → l12
  4. If(b ≟ 0, Sequence[Sequence[CurveCartesian[(i * sqrt(((c * d) - (4 * a)) / (d - a))), (j * sqrt((4 - c) / (d - a))), t, t, tmin, tmax], i, -1, 1, 2], j, -1, 1, 2]) → l3