Conic sections are formed by the intersection of a cone an plane. But how do we know that the shape developed by the plane is the same which we define in other ways.what i mean is that suppose the case of an ellipse . Let the plane intersection the cone at such an angle that an ellipse is formed.
Now prove to me that this shape is actually an ellipse by the definition that sum of distances from 2 points is constant. Similiarly prove for other definitions.