BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter B, Problem 50E
To determine

To calculate: To find the foci of the ellipse x2+4y2=4 and sketch its graph

Expert Solution

Answer to Problem 50E

The foci of ellipse are (3,0) and (3,0)

Explanation of Solution

Given information: Equation of ellipse is x2+4y2=4

Formula Used:

Standard equation of ellipse is

  x2a2+y2b2=1 ,

where c2=a2b2

Foci of above ellipse is (±c,0)

Calculation:

Equation of ellipse is given as

  x2+4y2=4

Rewrite the equation as follows:

  x24+4y24=44x24+y21=1x222+y212=1

On comparing the equation with standard equation of ellipse,

  a=2

  b=1

Value of c is calculated as follows:

  c2=a2b2c2=2212c2=41c2=3c=±3

Thus, foci of ellipse are (3,0) and (3,0)

On sketching the ellipse:

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter B, Problem 50E

Conclusion:

Hence, foci of ellipse are (3,0) and (3,0)

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