1. Take a look at Apollonius' Conics in the appendices. 2. Use Calculus to prove a property in Apollonius' book: Let C be a point on a hyperbola.Let CB be

the perpendicular from that point to the diameter. Let G and H be theintersections of the diameter with the curve, and choose A on the diameter, or thediameter extended, so that AH : AG = BH : BG. Then AC will be tangent to thecurve at C. As a special case with modern notation, we consider a hyperbola given by the equation 5- 6 = 1 with the intersection points with the real axis H = (3,0) and G = (-3,0).Let C = (-4, ) be a point in the hyperbola and B := (-4,0). If A = (xo,0) is a point such that the ratio of line segments AH/AG = BH/BG holds, we need to prove that the line passing through C and A is a tangent line of this hyperbola and need to find out