For ten points, an example of what conic section is the curve y equals x squared.
The inversion of this curve with respect to its focus is a cardioid, and with respect to its vertex the cissoid of Diocles.  More familiarly, it's those points where the distances between a line and a point not on the line are equal.  Rays parallel to the axis reflect from this curve to meet at the focus, a feature used in satellite dishes. For ten points, an example of what conic section is the curve y equals x squared.
The inversion of this curve with respect to its focus is a cardioid, and with respect to its vertex the cissoid of Diocles.  
parabola