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.