69. Constructing Points of a Hyperbola Use a geometry software package, such as Cabri Geometry II TM, The Geometer's Sketchpad®, or a similar application on a handheld device, to carry out the following construction.
(a) Start by placing the coordinate axes in the construction window.
(b) Construct two points on the x-axis at (±5,0) as the foci.
(c) Construct concentric circles of radii r=1,2,3,…,12 centered at these two foci.
(d) Construct the points where these concentric circles meet and have a difference of radii of 2a=6, and overlay the conic that passes through these points if the software has a conic tool.
(e) Find the equation whose graph includes all of these points.