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Chapter 10: Q 83 (page 669)

Two hyperbolas that have the same set of asymptotes are called conjugates. Show that the hyperbolas

x24-y2=1andy2-x24=1

are conjugate. Graph each hyperbola on the same set of coordinate axes.

Short Answer

Expert verified

The graph of the hyperbola is

Step by step solution

01

Step 1. Given Information

Two hyperbolas that have the same set of asymptotes are called conjugates. Show that the hyperbolas x24-y2=1andy2-x24=1are conjugate.

02

Step 2. Graph of the hyperbola 

x24-y2=1andy2-x24=1

The asymptote of 1st hyperbola is

y=卤baxy=卤12x

The asymptote of 2nd hyperbola is

y=卤abxy=卤12x

The asymptotes of both the hyperbolas are the same.

The graph of the hyperbola is

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Most popular questions from this chapter

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

2x2-3xy+2y2-4x-2=0

Rutherford鈥檚 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鈥檚 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 10cm from the center of the hyperbola, find a model that describes the path of the particle.

The graph of a parabola is given. Match each graph to its equation.

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus at -2,0and directix of the line x=2.

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus is at-4,0and vertex is at0,0.
See all solutions

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