What is the locus of a line passing through a fixed point and intersecting a hyperbola.We know that there are things like circular or elliptical cone if the generating line always intersects a circle or ellipse and passes through a fixed point.Is there anything like hyperbolic cone also.
I have another question,are the terms circular,elliptical etc for cone absolute in coordinate geometry?Because consider a cone through a fixed point and always intersecting a circle.Now we will call it a circular cone.But wait,we can find a plane that cut an ellipse from the cone(conic section).Now consider the locus of the line always passing through the vertex of this cone and intersecting this ellipse(obtained as a conic section),is the locus not the same cone,then it is now an elliptic cone.So I think these terms elliptic or circular are not very precise or absolute,because in coordinate geometry a cone has no so called base.[it is just a shape that spreads infinitely,it is not that cone that we find in elementary geometry having a base.]