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Unformatted text preview: d the distance in AU between the
sun and perihelion.
5. The graph of an ellipse clearly fails the Vertical Line Test, Theorem 1.1, so the equation of
an ellipse does not deﬁne y as a function of x. However, much like with circles and horizontal
parabolas, we can split an ellipse into a top half and a bottom half, each of which would
indeed represent y as a function of x. With the help of your classmates, use your calculator
to graph the ellipses given in Exercise 1 above. What diﬃculties arise when you plot them
on the calculator?
2 One might also say that the ellipse is “tangent to the axes” at those two points. 7.4 Ellipses 429 6. With the help of your classmates, research whispering galleries and other ways ellipses have
been used in architecture and design.
7. With the help of your classmates, research “extracorporeal shock-wave lithotripsy”. It uses
the reﬂective property of the ellipsoid to dissolve kidney stones. 430 7.4.2 Hooked on Conics Answers 1. (a) (b) (c) (d) x2
Center (0, 0)
Major axis along y = 0
Minor axis along x = 0
Vertices (13, 0), (−13, 0)
Foci (12, 0), (...
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