Kepler gave the follwoing construction for a hyperbola with foci at A and B and with one vertex at C: Let pins be placed at A and B. To A let a thread with length AC be tied and to B a thread with length BV. Let each tread be lenthened by an amount equal to itself. Then grasp the two threads together with one hand (starting with C) and little by little move away from C, paying out the two threads. With the other hand, draw the path of the join of the two threads at the fingers. Show that the path is a hyperbola.

Q: Find the coordinates of the foci for the following hyperbola. (x – 5)2 (y + 7)² = 1 16 25

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Q: Find the coordinates of the foci for the following hyperbola. (x – 1)? (y + 1)? 1 64 16

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