Chapter 10: Q60. (page 677)
How does your strategy presented in Problem 59 change if
the equation is of the following form:
Ax2 + Bxy + Cy2 + Dx + Ey
It is proved that
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Use the Square Root Method to find the real solutions of .
Rutherford’s Experiment In May 1911, Ernest Rutherford published a paper in Philosophical Magazine. In this article, he described the motion of alpha particles as they are shot at a piece of gold foil 0.00004 cm thick. Before conducting this experiment, Rutherford expected that the alpha particles would shoot through the foil just as a bullet would shoot through snow. Instead, a small fraction of the alpha particles bounced off the foil. This led to the conclusion that the nucleus of an atom is dense, while the remainder of the atom is sparse. Only the density of the nucleus could cause the alpha particles to deviate from their path. The figure shows a diagram from Rutherford’s paper that indicates that the deflected alpha particles follow the path of one branch of a hyperbola.
(a) Find an equation of the asymptotes under this scenario.
(b) If the vertex of the path of the alpha particles is cm from the center of the hyperbola, find a model that describes the path of the particle.
In Problems 19–28, find an equation for the hyperbola described. Graph the equation by hand. Center at ; focus at ; vertex at.
Lightning Strikes Suppose that two people standing mile apart both see a flash of lightning. After a period of time, the first person standing at point hears the thunder. Two seconds later, the second person standing at point hears the thunder. If the person at point is due west of the person at point and if the lightning strike is known to occur due north of the person standing at point , where did the lightning strike occur?
True or False
The equation defines a parabola if.
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