The picture on the right shows a red ellipse, which is tangent to four blue ellipses and a blue hyperbola. The question of how many conics are tangent to five given conics is known as Steiner's conic problem.
Follow this link, if you want to compute the conics that are tangent to your five personal conics:
Looking at data through the lens of algebraic geometry
Algebraic methods yield insight into the geometry of datasets: in a world where huge amounts of information are released and collected every day, it has become essential to be able to give meaning to data sets and to recognise any underlying pattern in the collected data.