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 20MCQ
To determine

To find: find the equation of the ellipse.

Expert Solution & Answer
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Answer to Problem 20MCQ

The equation of an ellipse is (y2)264+(x+4)236=1

Explanation of Solution

Given information:

The given endpoints of ellipse is,

  (4,10),(4,6)

And foci

  (4,7.3) , (4,3.3)

The midpoint of an ellipse is the centre of the circle is calculated as,

The given endpoints are

  (x1=4,y1=10) and (x2=4,y2=6)

Simplify,

  M=x1+x22,y1+y22M=4+(4)2,10+(6)2M=4,2

The centre of the ellipse is (4,2)

The length of the major axis is

  2a=10(6)a=8

The distance of the foci is

Foci= 2c

  2c=7.3(3.3)c=5.3

The relation of between a,b and c are

  a2b2=c2(8)2b2=(5.3)2b2=6428b=6

By using the equation of an ellipse with vertical major axis,

  (yk)2a2+(xh)2b2=1....(2)

Put the values of h=4,k=2 and a=8,b=6 in the equation (2),

  (yk)2a2+(xh)2b2=1(y2)282+(x(4))262=1(y2)264+(x+4)236=1

Thus, the equation (H) represents an ellipse.

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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