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 34PPS
To determine

To write: The equation for the given ellipse.

Expert Solution & Answer
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Answer to Problem 34PPS

The equation for the given ellipse is (x−4)229+(y+3)24=1 .

Explanation of Solution

Given information:

The focus of the ellipse is at (9,−3) , the co-vertices is at (4,−5) , and the centre is at (4,−3) .

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 value of h and k from the centre is,

  h=4k=−3

The value of b from the covertexand the focus is calculated as,

  b=(−3)−(−5)b=2

The value of c is calculated as,

  c=9−4=5

The value of a is calculated as,

  c=a2−b25=a2−22a=29

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

  (x−h)2a2+(y−k)2b2=1(x−4)2(29)2+(y−(−3))2(2)2=1(x−4)229+(y+3)24=1

Thus, the equation for the given ellipse is (x−4)229+(y+3)24=1 .

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Chapter 10.4, Problem 33PPS
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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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Prob. 8CYUCh. 10.4 - Prob. 9CYUCh. 10.4 - Prob. 10CYUCh. 10.4 - Prob. 11PPSCh. 10.4 - Prob. 12PPSCh. 10.4 - Prob. 13PPSCh. 10.4 - Prob. 14PPSCh. 10.4 - Prob. 15PPSCh. 10.4 - Prob. 16PPSCh. 10.4 - Prob. 17PPSCh. 10.4 - Prob. 18PPSCh. 10.4 - Prob. 19PPSCh. 10.4 - Prob. 20PPSCh. 10.4 - Prob. 21PPSCh. 10.4 - Prob. 22PPSCh. 10.4 - Prob. 23PPSCh. 10.4 - Prob. 24PPSCh. 10.4 - Prob. 25PPSCh. 10.4 - Prob. 26PPSCh. 10.4 - Prob. 27PPSCh. 10.4 - Prob. 28PPSCh. 10.4 - Prob. 29PPSCh. 10.4 - Prob. 30PPSCh. 10.4 - Prob. 31PPSCh. 10.4 - Prob. 32PPSCh. 10.4 - Prob. 33PPSCh. 10.4 - Prob. 34PPSCh. 10.4 - Prob. 35PPSCh. 10.4 - Prob. 36PPSCh. 10.4 - Prob. 37PPSCh. 10.4 - Prob. 38PPSCh. 10.4 - Prob. 39PPSCh. 10.4 - Prob. 40HPCh. 10.4 - Prob. 41HPCh. 10.4 - Prob. 42HPCh. 10.4 - Prob. 43HPCh. 10.4 - Prob. 44HPCh. 10.4 - Prob. 45HPCh. 10.4 - Prob. 46HPCh. 10.4 - Prob. 47STPCh. 10.4 - Prob. 48STPCh. 10.4 - Prob. 49STPCh. 10.4 - Prob. 50STPCh. 10.4 - Prob. 51SRCh. 10.4 - Prob. 52SRCh. 10.4 - Prob. 53SRCh. 10.4 - 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