Tangent-Conics

1. Construct tangents to a circle from a point outside.
   
   

2. From a point lying on the tangent of a parabola, construct the second tangent.
   
   

3. Through any suitable point, construct the pair of tangents of a given parabola.
   
   

4. From a point lying on the tangent of an ellipse, construct the second tangent.
   
   

5. Through any suitable point, construct the pair of tangents of a given ellipse.
   
   

6. Through any suitable point, construct the pair of tangents of a given hyperbola.
   
   

7. Construct the tangent through a point lying on the ellipse which is constructed according the the paramentric equations.
   
   

8. Here is another way to construct an ellipse.

   1. Draw a circle and two straight lines and
      
      

   2. From a variable point of the circle construct a line parallel to meeting at the point
      
      

   3. With as center, rotate by to point
      
      

   4. Construct the locus of as varies over the circle.
      
      Construct the tangent to the ellipse through the point by mapping the tangent at to the circle.
      
      

9. If the ellipse were constructed as above, construct the two tangents passing through any suitable given point.
   
   

10. Construct the pair of tangents through a suitable point to the ellipse which is constructed according the the paramentric equations.
    
    

11. Construct the tangent through a point lying on the hyperbola which is constructed according the the paramentric equations.
    
    

12. Construct the pair of tangents through a suitable point to the hyperbola which is constructed according the the paramentric equations.