Why We Study Hyperbola?

A hyperbola is a pair of symmetrical open curves. It is what we get when we slice a pair of vertical joined cones with a vertical plane.

How can we obtain a hyperbola from slicing a cone?

We start with a double cone (2 right circular cones placed apex to apex):

When we slice the 2 cones vertically, we get a hyperbola, as shown:                                                                                                                                                                                                        

Cooling towers for a nuclear power plant have a hyperbolic cross-section

How do we create a hyperbola?

Take 2 fixed points A and B and let them be 4a units apart. Now, take half of that distance (i.e. 2a units).

Now, move along a curve such that from any point on the curve,

(distance to A) − (distance to B) = 2a units.

The curve that results is called a hyperbola. There are two parts to the curve.