Geometric Construction 1

1. An ellipse is the locus of a point which moves so that the sum of its distances from two fixed points (the loci) is a constant. Construct the ellipse according to this definition.

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2.  A hyperbola is the locus of a point which moves so that the difference of its distances from two fixed points (the loci) is a constant. Construct the hyperbola according to this definition.

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3. A parabola is the locus of a point which moves so that the sum of its distances a fixed point (the locus) to a fixed straight line (the directrix) is a constant. Construct the parabola according to this definition.

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4. Construct an animation displaying various positions of a pair of orthogonal tangents to an ellipse. Find the locus of the point of intersection of these two tangents.

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5. Construct an animation displaying various positions of a pair of orthogonal tangents to a hyperbola. Find the locus of the point of intersection of these two tangents.

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6. Construct an animation displaying various positions of a pair of orthogonal tangents to an ellipse. Find the locus of the point of intersection of these two tangents.

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7. From a given point lying outside an ellipse, construct the pair of tangents passing through the point.

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8. From a given point lying ``between'' the hyperbola, construct the pair of tangents passing through the point.

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9. From a given point lying ``under'' a parabola, construct the pair of tangents passing through the point.

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