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Chapter 10: Q. 8 (page 667)

For a hyperbola, the foci lie on a line called the _______________

Short Answer

Expert verified

For a hyperbola, the foci lie on a line called the Transverse axis.

Step by step solution

01

Step 1. Concept

A Hyperbola is the collection of all points in the plane, the difference of whose

distances from two fixed points, called the foci, is a constant.

The above figure is the graph of the hyperbolax29-y216=1with focii at (5,0)and (-5,0).

The line containing the foci is called the Transverse axis.

Here the foci lie on the x-axis . Hence here the transverse axis is thex-axis.

02

Step 2. Conclusion

For a hyperbola, the foci lie on a line called the Transverse axis.

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Most popular questions from this chapter

Semi elliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20meters wide. The center of the arch is 6meters above the center of the river. See the figure. Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch.

Hyperbolic Mirrors Hyperbolas have interesting reflective properties that make them useful for lenses and mirrors. For example, if a ray of light strikes a convex hyperbolic mirror on a line that would (theoretically) pass through its rear focus, it is reflected through the front focus. This property, and that of the parabola, were used to develop the Cassegrain telescope in 1672. The focus of the parabolic mirror and the rear focus of the hyperbolic mirror are the same point. The rays are collected by the parabolic mirror, reflected toward the (common) focus, and thus are reflected by the hyperbolic mirror through the opening to its front focus, where the eyepiece is located. If the equation of the hyperbola is y29-x216=1 and the focal length (distance from the vertex to the focus) of the parabola is 6, find the equation of the parabola.

Projectile Motion Suppose that Adam hits a golf ball off a cliff 300 meters high with an initial speed of 40 meters per second at an angle of 45掳 to the horizontal.

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Source: The Boston Red Sox

A(n)__________ is the collection of all points in the plane such that the distance from each point to a fixed point equals its distance to a fixed line.
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