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Chapter 10: Q. 35 (page 668)

In Problems 29–36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation by hand. Verify your graph using a graphing utility.y2-x2=25

Short Answer

Expert verified

Center:(0,0)Transverseaxis:y-axisVertices:(0,±5)Foci:(0,±52)Asymptotes:y=±x

Graph of the equation is:

Step by step solution

01

Step 1. Given information 

Equation of hyperbola, y2-x2=25

Writing the equation in standard form,y225-x225=1

02

Step 2. Finding the center, transverse axis, vertices, foci, and asymptotes of hyperbola

Comparing the given equation with standard form, y2a2-x2b2=1,b2=c2-a2

We get,

a=5,b=5,c=±a2+b2⇒c=±52+52⇒c=±25+25⇒c=±50⇒c=±52

Center:(0,0)Transverseaxis:y-axisVertices:(0,±a)=(0,±5)Foci:(0,±c)=(0,±52)Asymptotes:y=±abx⇒y=±55x⇒y=±x

03

Step 3. Graph of the equation

Graph of the equation is:

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Most popular questions from this chapter

Semi elliptical Arch Bridge: A bridge is built in the shape of a semi elliptical arch. The bridge has a span of 120feet and a

maximum height of 25feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances

of 10,30and 50feet from the center.

Answer the following problem using the figure,

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a)y-k2=4ax-hb)y-k2=-4ax-hc)x-h2=4ay-kd)x-h2=-4ay-k

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.

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Answer Problem using the figure.

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