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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Question
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Chapter 10.6, Problem 43PPS

a.

To determine

Find the standard form of the equation.

a.

Expert Solution
Check Mark

Answer to Problem 43PPS

  (x−3)216+(y+2)24=1

Explanation of Solution

Given information:

An ellipse with centre (3,−2), vertex M(−1,−2), and co-vertex N(3,−4).

Calculation:

As the y− ordinate of vertex and centre is same, the ellipse is horizontal.

Value of a will be the distance between vertex and centre.

  a=3−(−1)=4

Value of b will be equal to the distance between co-vertex and centre.

  b=(−2)−(−4)=2

Use the equation of an ellipse with horizontal orientation,

  (x−h)2a2+(y−k)2b2=1

Substitute (h,k)=(3,−2),a=4,b=2 , the equation of given ellipse will be,

  (x−3)242+{y−(−2)}222=1

  (x−3)216+(y+2)24=1

b.

To determine

Convert in standard form.

b.

Expert Solution
Check Mark

Answer to Problem 43PPS

  x2+4y2−6x+16y+9=0

Explanation of Solution

Given information:

An ellipse with centre (3,−2), vertex M(−1,−2), and co-vertex N(3,−4).

  Ax2+Bxy+Cy2+Dx+Ey+F=0

Calculation:

Convert the equation (1)(x−3)216+(y+2)24=1 to standard form

  (x−3)216+(y+2)24=1(x−3)2+4(y+2)2=16x2−6x+9+4y2+16y+16=16x2+4y2−6x+16y+9=0

Hence, standard form of the equation of ellipse is,

  x2+4y2−6x+16y+9=0

c.

To determine

Graph the ellipse.

c.

Expert Solution
Check Mark

Answer to Problem 43PPS

  Algebra 2, Chapter 10.6, Problem 43PPS , additional homework tip 1

Explanation of Solution

Given information:

An ellipse with centre (3,−2), vertex M(−1,−2), and co-vertex N(3,−4).

Calculation:

The graph is shown below:

  Algebra 2, Chapter 10.6, Problem 43PPS , additional homework tip 2

d.

To determine

Determine the location of N and the angle of rotation.

d.

Expert Solution
Check Mark

Answer to Problem 43PPS

Explanation of Solution

Given information:

An ellipse with centre (3,−2), vertex M(−1,−2), and co-vertex N(3,−4).

Calculation:

Distance between new position of point M and centre will be,

  (−2)−(−6)=4

By rotating the ellipse in the given manner, the horizontal ellipse will be the “Vertical ellipse”.

Hence, the angle of rotation will be 90°counterclockwise

The new position of point N will have same y−ordiante as of centre and its x−ordinate will be,

  (−2)−(−6)=4

Hence, the new position of point N will be (5,−2) .

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Chapter 10.6, Problem 42PPS
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Chapter 10.6, Problem 44HP

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. 11SGRCh. 10 - Prob. 12SGRCh. 10 - Prob. 13SGRCh. 10 - Prob. 14SGRCh. 10 - Prob. 15SGRCh. 10 - Prob. 16SGRCh. 10 - Prob. 17SGRCh. 10 - Prob. 18SGRCh. 10 - Prob. 19SGRCh. 10 - Prob. 20SGRCh. 10 - Prob. 21SGRCh. 10 - Prob. 22SGRCh. 10 - Prob. 23SGRCh. 10 - Prob. 24SGRCh. 10 - Prob. 25SGRCh. 10 - Prob. 26SGRCh. 10 - Prob. 27SGRCh. 10 - Prob. 28SGRCh. 10 - Prob. 29SGRCh. 10 - Prob. 30SGRCh. 10 - Prob. 31SGRCh. 10 - Prob. 32SGRCh. 10 - Prob. 33SGRCh. 10 - Prob. 34SGRCh. 10 - Prob. 35SGRCh. 10 - Prob. 36SGRCh. 10 - Prob. 37SGRCh. 10 - Prob. 38SGRCh. 10 - Prob. 39SGRCh. 10 - Prob. 40SGRCh. 10 - Prob. 41SGRCh. 10 - Prob. 42SGRCh. 10 - Prob. 43SGRCh. 10 - Prob. 44SGRCh. 10 - Prob. 45SGRCh. 10 - Prob. 46SGRCh. 10 - Prob. 47SGRCh. 10 - Prob. 48SGRCh. 10 - Prob. 49SGRCh. 10 - Prob. 50SGRCh. 10 - Prob. 51SGRCh. 10 - Prob. 52SGRCh. 10 - Prob. 53SGRCh. 10 - Prob. 54SGRCh. 10 - Prob. 55SGRCh. 10 - Prob. 56SGRCh. 10 - Prob. 57SGRCh. 10 - Prob. 58SGRCh. 10 - Prob. 59SGRCh. 10 - Prob. 60SGRCh. 10 - Prob. 61SGRCh. 10 - Prob. 62SGRCh. 10 - Prob. 63SGRCh. 10 - Prob. 64SGRCh. 10 - Prob. 65SGRCh. 10 - Prob. 66SGRCh. 10 - Prob. 67SGRCh. 10 - Prob. 68SGRCh. 10 - Prob. 69SGRCh. 10 - Prob. 70SGRCh. 10 - Prob. 71SGRCh. 10 - Prob. 72SGRCh. 10 - Prob. 73SGRCh. 10 - Prob. 74SGRCh. 10 - Prob. 1PTCh. 10 - Prob. 2PTCh. 10 - Prob. 3PTCh. 10 - Prob. 4PTCh. 10 - Prob. 5PTCh. 10 - Prob. 6PTCh. 10 - Prob. 7PTCh. 10 - Prob. 8PTCh. 10 - Prob. 9PTCh. 10 - Prob. 10PTCh. 10 - Prob. 11PTCh. 10 - Prob. 12PTCh. 10 - Prob. 13PTCh. 10 - Prob. 14PTCh. 10 - Prob. 15PTCh. 10 - Prob. 16PTCh. 10 - Prob. 17PTCh. 10 - Prob. 18PTCh. 10 - Prob. 19PTCh. 10 - Prob. 20PTCh. 10 - Prob. 21PTCh. 10 - Prob. 22PTCh. 10 - Prob. 23PTCh. 10 - Prob. 24PTCh. 10 - Prob. 25PTCh. 10 - Prob. 1ECh. 10 - Prob. 2ECh. 10 - Prob. 3ECh. 10 - Prob. 4ECh. 10 - Prob. 5ECh. 10 - Prob. 1STPCh. 10 - Prob. 2STPCh. 10 - Prob. 3STPCh. 10 - Prob. 4STPCh. 10 - Prob. 5STPCh. 10 - Prob. 6STPCh. 10 - Prob. 7STPCh. 10 - Prob. 8STPCh. 10 - Prob. 9STPCh. 10 - Prob. 10STPCh. 10 - Prob. 11STPCh. 10 - Prob. 12STPCh. 10 - Prob. 13STPCh. 10 - Prob. 14STPCh. 10 - Prob. 15STP

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