Geometric Construction 2

• Construct the conic given two foci and one tangent. Under what condition is the conic an ellipse? A hyperbola?

• Given the focus and two tangents, construct the parabola.

• Given two foci and one point, construct an ellipse passing through the point.

• Given two foci and one point, construct a hyperbola passing through the point.

  

• Given the axis, the focus and one point, construct the parabolas passing through the point.

 

• Given a parabola, construct an animation displaying all orthogonal parabolas sharing the same focus and axis.

• Through a point on a given ellipse, construct a hyperbola sharing the same foci, passing through the point and orthogonal to it at the point.

• Through a point on a given hyperbola, construct an ellipse sharing the same foci, passing through the point and orthogonal to it at the point.