*…show more content…*

It's equation is: (x-h)2a2+(y-k)2b2=1. AC> 0to create an ellipse when B = 0. Additionally, if the plane cuts through the cone at an angle that is the same as the surface of the cone, it will from a parabola. A parabola can be considered as a locus of points that are each equidistant from a directrix, which is a given line, and a focus, which is a given point. If B = 0, then A must equal 0 or C must equal 0 but not both. The equation of a horizontal hyperbola is: y-k=14p(x-h)2and x-h=14p(y-k)2for a vertical ellipse. In this situation, the a value is 14p. Finally, a hyperbola can be formed by tilting the plane at an angle much higher than the surface of the cone. This creates the equation (x-h)2a2-(y-k)2b2=1for horizontal hyperbolas and (y-k)2a2 -(x-h)2b2=1for vertical hyperbolas. A hyperbola is a locus of points with a fixed difference from the two given foci. This distance between the hyperbola and the foci is given. AC