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Chapter 10: Q. 26 (page 667)

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Vertices at (-4,0)and (4,0); asymptote the liney=2x.

Short Answer

Expert verified

Equation of the hyperbola:x216-y264=1

Graph of the hyperbola:

Step by step solution

01

Step 1. Given information 

Hyperbola with vertices at (-4,0)and role="math" localid="1646997921363" (4,0); asymptote the liney=2x.

02

Step 2. Required to find 

Find the equation of the hyperbola. Graph the equation.

03

Step 3. Finding the equation of the hyperbola 

Given, hyperbola with vertices at (-4,0)and (4,0); asymptote the line y=2x.

Comparing with standard form of hyperbola, x2a2-y2b2=1,b2=c2-a2;vertices=(卤a,0);asymptotes,y=卤bax

We get,

a=4,ba=2鈬�b=2a鈬�b=2脳4鈬�b=8

Substituting aand bin the equation,

x216-y264=1

04

Step 4. Graphing the hyperbola 

Graph of the hyperbola:

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Most popular questions from this chapter

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

and equations are,

A)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)

In Problems 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40.

3x2-10xy+3y2-32=0

In Problem, identify the graph of each equation without completing the squares.

6x2+3y2-12x+6y=0

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Center at (0,0); focus at (3,0); vertex at(1,0).

Answer Problem using the figure.

If a = 4, then the coordinates of the focus are___________.
See all solutions

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