The set of intersections of two conic sections can be determined computationally or graphically.
The set of intersections of two cones is represented by the solution of a system of two quadratic equations with two unknowns 
and 
:
The system of two quadratic equations with two unknowns is generally solved by:
subtract the square of one of the unknowns from both equations (by the method of opposite coefficients or by the alternating method of solving equations with two unknowns),
from the obtained equation we express the unknown whose square we have excluded,
We insert the expression into one of the equations instead of this unknown.
Graphically determine the intersection of the conics by drawing the conics in the same coordinate system and reading the intersections from the graph.
