Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

Vertices Of An Ellipse
In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…
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Chapter 10.4, Problem 32PPS
To determine

To write: an equation relating the comet’s orbit around the sun in millions of miles with the centre of the horizontal ellipse at the origin.

Expert Solution & Answer
Check Mark

Answer to Problem 32PPS

The equation for the given ellipse is x2(1672.82)2+y2(426.58)2=1 .

Explanation of Solution

Given information:

The given aphelion of the elliptical orbit of the sun is 3282.9 millions miles and perihelion is 54.87 millions miles .

Concept used:

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

  (x−h)2a2+(y−k)2b2=1

The coordinate of the foci is (h±c,k)

The value of c is calculated as,

  c=a2−b2

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,

  (y−k)2a2+(x−h)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=a2−b2

The planet Halley’s Comet travels around the sun in elliptical orbit.

The aphelion of the elliptical orbit of the sun is 3282.9 millions miles and perihelion is 54.87 millions miles

The diameter of the sun is 0.87 millions miles

The length of major axis of the ellipse is the sum of aphelion, perihelion and sun’s diameter.

Simplify as,

  2a=3282.9+54.87+0.872a=3345.64a=1672.82 millions miles

The focus of the centre is the value of a=1672.82 minus the sum of radius of the sun and perihelion

  c=1672.82−(0.872+54.87)c=1672.82−55.305c=1617.515

To calculate the value of b by using the relations between of the a, b and c is

  a2−b2=c2

  (1672.82)2−b2=(1617.515)22798326.7524−b2=2616354.775225b2=181971.977175b=426.58

The standard form of the equation at the given origin centre of the elliptical orbit of the planet Halley’s comet is,

  x2a2+y2b2=1x2(1672.82)2+y2(426.58)2=1

Thus, the equation for the given ellipse is x2(1672.82)2+y2(426.58)2=1 .

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Chapter 10.4, Problem 31PPS
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Chapter 10.4, Problem 33PPS

Chapter 10 Solutions

Algebra 2

Ch. 10.1 - Prob. 1ACYPCh. 10.1 - Prob. 1BCYPCh. 10.1 - Prob. 2CYPCh. 10.1 - Prob. 3CYPCh. 10.1 - Prob. 1CYUCh. 10.1 - Prob. 2CYUCh. 10.1 - Prob. 3CYUCh. 10.1 - Prob. 4CYUCh. 10.1 - Prob. 5CYUCh. 10.1 - Prob. 6CYU
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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College Algebra (7th Edition)

In the following exercises, divide. Then check by multiplying. 855,305

PREALGEBRA

Complete the square to make a perfect square trinomial. Write the result as a binomial square. p2+14p

Elementary Algebra

For each subspace in Exercises 1-8, (a) find a basis, and (b) state the dimension. 5. {[a4b2c2a+5b4ca+2c3a+7b+6...

Linear Algebra and Its Applications (5th Edition)

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What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY