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 6CYU
To determine

To find: The equation relating Earth’s orbit around the Sun in millions of miles.

Expert Solution & Answer
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Answer to Problem 6CYU

The equation relating Earth’s orbit around the Sun in millions of miles is x2(93.385)2+y2(93.37)2=1

Explanation of Solution

Given information:

Earth’s orbit is about 91.4millon miles at perihelion and about 94.5millon miles at aphelion.

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

The diameter of the Sun is 0.87million miles.

The value of a is calculated as,

  2a=0.87+91.4+94.52a=186.77a=93.385million miles

The value of c is calculated as,

  c=93.385(91.4+0.872)=1.55million miles

The value of b is calculated as,

  c=a2b21.55=(93.385)2b2b=93.37million miles

The standard form of the equation of the given ellipse is,

  (xh)2a2+(yk)2b2=1(x0)2(93.385)2+(y0)2(93.37)2=1x2(93.385)2+y2(93.37)2=1

Thus, the equation for the given ellipse is x2(93.385)2+y2(93.37)2=1 .

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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