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Chapter 10: Q. 35 (page 668)

In Problems 29鈥�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,卤5)Foci:(0,卤52)Asymptotes:y=卤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=卤a2+b2鈬�c=卤52+52鈬�c=卤25+25鈬�c=卤50鈬�c=卤52

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

03

Step 3. Graph of the equation

Graph of the equation is:

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Most popular questions from this chapter

Except for degenerate cases, the equationAx2+Bxy+Cy2+Dx+Ey+F=0defines an ellipse if ________ .

Find an equation for each ellipse. Graph the equation by hand.

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