Geometric Construction 1

1. An ellipse is defined as the set of points, the sum of whose distances from two fixed points is constant. Construct an ellipse from its definition.
   
   
   
   

2. The hyperbola is defined as the set of points, the difference of whose distances from two fixed points is constant. Construct the hyperbola from its definition.
   
   

3. The parabola is defined as the set of points whose distance from a fixed point is the same as whose distance from a fixed line. Construct the parabola from its definition.
   
   
   
   
   
   

4. Construct an ellipse from the parametric equations
   
   

5. Find parametric equations for the hyperbola
   
   Construct the hyperbola based on the parametric equations.

6. Construct a pair of tangents through a given point lying outside a given ellipse.
   
   

7. Suppose that the ellipse were constructed based on the parametric equations, Construct a pair of tangents through a given point lying outside the ellipse.

8. Construct a pair of tangents through a given point lying ``outside'' a parabola.