Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 10.4, Problem 27PPS
To determine

To find: The coordinates of the centre and foci and the length of the major and minor axis for the given ellipse.

Expert Solution & Answer
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Answer to Problem 27PPS

the coordinates of the centre and foci are (4,0) and (4,±59) , the length of the major axis is 103unit , and the length of the minor axis is 8unit.

Explanation of Solution

Given information:

The equation of the ellipse is,

  (x+4)216+y275=1

Concept used:

Write the standard form of the equation of the ellipse whose orientation is along the horizontal axis is,

  (xh)2a2+(yk)2b2=1

The coordinate of the foci is (h±c,k)

The value of c is calculated as,

  c=a2b2

The vertices are at (h±a,k) and the co-vertices are at (h,k±b).

Write the standard form of the equation of the ellipse whose orientation is along the vertical axis is,

  (yk)2a2+(xh)2b2=1

The coordinate of the foci is (h,k±c)

The vertices are at (h,k±a) and the co-vertices are at (h±b,k).

The value of c is calculated as,

  c=a2b2

Write the standard form of the equation of the ellipse whose orientation is along the vertical axis is,

  (yk)2a2+(xh)2b2=1

Compare the given equation with the standard form of the equation to obtain,

  h=4k=0a2=75a=53

  b2=16b=4

The length of the major axis is calculated as,

  2a=2×532a=103unit

The length of the minor axis is calculated as,

  2b=2×42b=8unit

The value of c is calculated as,

  c=a2b2=7516=59unit

The coordinate of the foci is calculated as,

  (h,k±c)=(4,±59)

Consider the following graph of the ellipse as,

  Algebra 2, Chapter 10.4, Problem 27PPS

Thus, the coordinates of the centre and foci are (4,0) and (4,±59) , the length of the major axis is 103unit , and the length of the minor axis is 8unit.

Chapter 10 Solutions

Algebra 2

Ch. 10.1 - Prob. 7CYUCh. 10.1 - Prob. 8CYUCh. 10.1 - Prob. 9CYUCh. 10.1 - Prob. 10PPSCh. 10.1 - Prob. 11PPSCh. 10.1 - Prob. 12PPSCh. 10.1 - Prob. 13PPSCh. 10.1 - Prob. 14PPSCh. 10.1 - Prob. 15PPSCh. 10.1 - Prob. 16PPSCh. 10.1 - Prob. 17PPSCh. 10.1 - Prob. 18PPSCh. 10.1 - Prob. 19PPSCh. 10.1 - Prob. 20PPSCh. 10.1 - Prob. 21PPSCh. 10.1 - Prob. 22PPSCh. 10.1 - Prob. 23PPSCh. 10.1 - Prob. 24PPSCh. 10.1 - Prob. 25PPSCh. 10.1 - Prob. 26PPSCh. 10.1 - Prob. 27PPSCh. 10.1 - Prob. 28PPSCh. 10.1 - Prob. 29PPSCh. 10.1 - Prob. 30PPSCh. 10.1 - Prob. 31PPSCh. 10.1 - Prob. 32PPSCh. 10.1 - Prob. 33PPSCh. 10.1 - Prob. 34PPSCh. 10.1 - Prob. 35PPSCh. 10.1 - Prob. 36PPSCh. 10.1 - Prob. 37PPSCh. 10.1 - Prob. 38PPSCh. 10.1 - Prob. 39PPSCh. 10.1 - Prob. 40PPSCh. 10.1 - Prob. 41PPSCh. 10.1 - Prob. 42HPCh. 10.1 - Prob. 43HPCh. 10.1 - Prob. 44HPCh. 10.1 - Prob. 45HPCh. 10.1 - Prob. 46HPCh. 10.1 - Prob. 47STPCh. 10.1 - Prob. 48STPCh. 10.1 - Prob. 49STPCh. 10.1 - Prob. 50STPCh. 10.1 - Prob. 51SRCh. 10.1 - Prob. 52SRCh. 10.1 - 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