47. Consider the general hyperbola with foci Fi (0) and F(-c0) and vertices Vi(a,0) and V(-a,0). This hyperbola is cente

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47 Consider The General Hyperbola With Foci Fi 0 And F C0 And Vertices Vi A 0 And V A 0 This Hyperbola Is Cente 1 (32.41 KiB) Viewed 36 times

47. Consider the general hyperbola with foci Fi (0) and F(-c0) and vertices Vi(a,0) and V(-a,0). This hyperbola is centered at the origin and symmetric about the x and y-axes. Com- plete the following steps to derive the equation of the hyperbola. (a) Let P(x,y) be a point on the right branch of the hyperbola. Show that d(PF) -d(PF) = 2a. (b) Show that = 1 gives the equation of the hyperbola. a ? 52 00 a (c) Suppose y > 0 and show that lim = 0. Conclude that the asymptotes x² y² b for the hyperbola 1 are given by y=+-r. a2 (d) Suppose P is on the left branch of the hyperbola. What is d(PF) - d(PF) in this case? a