Precalculus
Precalculus
9th Edition
ISBN: 9780321716835
Author: Michael Sullivan
Publisher: Addison Wesley
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Chapter 10.5, Problem 8AYU
To determine

The choice in the blank for the following statement

The equation ax2+6y2+12y=0 defines an ellipse if _

  1. a<0

  2. a=0

  3. a>0

  4. a is any real number.

Expert Solution & Answer
Check Mark

Answer to Problem 8AYU

Solution:

The equation ax2+6y2+12y=0 defines an ellipse, if a>0

Explanation of Solution

Given information:

The equation is ax2+6y2+12y=0

Explanation:

The equation Ax2+Cy2+Dx+Ey+F=0, where A and C are not both equal to zero defines an ellipse, if AC>0

Compare the equation ax2+6y2+12y=0 and ax2+6y2+12y=0, get

A=a and C=6

Implies that AC=6a

Since the equation defines a ellipse, when AC>0, that is when 6a>0

Dividing both sides of 6a>0 by 6

a>0

Therefore, the equation ax2+6y2+12y=0 defines an ellipse if a>0

Chapter 10 Solutions

Precalculus

Ch. 10.2 - In Problems 13-20, the graph of a parabola is...Ch. 10.2 - In Problems 13-20, the graph of a parabola is...Ch. 10.2 - In Problems 13-20, the graph of a parabola is...Ch. 10.2 - In Problems 13-20, the graph of a parabola is...Ch. 10.2 - In Problems 13-20, the graph of a parabola is...Ch. 10.2 - In Problems 13-20, the graph of a parabola is...Ch. 10.2 - In Problems 13-20, the graph of a parabola is...Ch. 10.2 - In Problems 13-20, the graph of a parabola is...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems 21-38, find the equation of the...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems 3956, find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems 3956, find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems 3956, find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems 3956, find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems 3956, find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems , find the vertex, focus, and...Ch. 10.2 - In Problems 57-64, write an equation for each...Ch. 10.2 - In Problems 57-64, write an equation for each...Ch. 10.2 - In Problems 57-64, write an equation for each...Ch. 10.2 - In Problems 57-64, write an equation for each...Ch. 10.2 - In Problems 57-64, write an equation for each...Ch. 10.2 - In Problems 57-64, write an equation for each...Ch. 10.2 - In Problems 57-64, write an equation for each...Ch. 10.2 - In Problems 57-64, write an equation for each...Ch. 10.2 - Satellite Dish A satellite dish is shaped like a...Ch. 10.2 - Prob. 64AYUCh. 10.2 - Prob. 65AYUCh. 10.2 - Prob. 66AYUCh. 10.2 - Prob. 67AYUCh. 10.2 - Prob. 68AYUCh. 10.2 - Prob. 69AYUCh. 10.2 - Prob. 70AYUCh. 10.2 - Prob. 71AYUCh. 10.2 - Prob. 72AYUCh. 10.2 - Prob. 73AYUCh. 10.2 - Prob. 74AYUCh. 10.2 - Prob. 75AYUCh. 10.2 - Prob. 76AYUCh. 10.2 - Prob. 77AYUCh. 10.2 - Prob. 78AYUCh. 10.2 - Prob. 79AYUCh. 10.3 - The distance d from P 1 =( 2,5 ) to P 2 =( 4,2 )...Ch. 10.3 - To complete the square of x 2 3x , Add _____. 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In Problems, find the center , transverse axis,...Ch. 10.4 - In Problems 2936, find the center, transverse...Ch. 10.4 - In Problems 2936, find the center, transverse...Ch. 10.4 - In Problems, find the center, transverse axis,...Ch. 10.4 - In Problems 2936, find the center, transverse...Ch. 10.4 - In Problems, find the center, transverse axis,...Ch. 10.4 - In Problems 2936, find the center, transverse...Ch. 10.4 - In Problems 37-40, write an equation for each...Ch. 10.4 - In Problems 37-40, write an equation for each...Ch. 10.4 - In Problems 37-40, write an equation for each...Ch. 10.4 - In Problems 37-40, write an equation for each...Ch. 10.4 - In Problems 41-48, find an equation for the...Ch. 10.4 - In Problems 41-48, find an equation for the...Ch. 10.4 - In Problems 41-48, find an equation for the...Ch. 10.4 - In Problems 41-48, find an equation for the...Ch. 10.4 - In Problems 41-48, find an equation for the...Ch. 10.4 - In Problems 41-48, find an equation for the...Ch. 10.4 - In Problems 41-48, find an equation for the...Ch. 10.4 - 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Prob. 9AYUCh. 10.5 - Prob. 10AYUCh. 10.5 - Prob. 11AYUCh. 10.5 - Prob. 12AYUCh. 10.5 - Prob. 13AYUCh. 10.5 - Prob. 14AYUCh. 10.5 - Prob. 15AYUCh. 10.5 - Prob. 16AYUCh. 10.5 - Prob. 17AYUCh. 10.5 - Prob. 18AYUCh. 10.5 - Prob. 19AYUCh. 10.5 - Prob. 20AYUCh. 10.5 - Prob. 21AYUCh. 10.5 - Prob. 22AYUCh. 10.5 - Prob. 23AYUCh. 10.5 - Prob. 24AYUCh. 10.5 - Prob. 25AYUCh. 10.5 - Prob. 26AYUCh. 10.5 - Prob. 27AYUCh. 10.5 - Prob. 28AYUCh. 10.5 - Prob. 29AYUCh. 10.5 - Prob. 30AYUCh. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - Prob. 35AYUCh. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - In Problems 31-42, rotate the axes so that the new...Ch. 10.5 - Prob. 43AYUCh. 10.5 - Prob. 44AYUCh. 10.5 - Prob. 45AYUCh. 10.5 - Prob. 46AYUCh. 10.5 - Prob. 47AYUCh. 10.5 - Prob. 48AYUCh. 10.5 - Prob. 49AYUCh. 10.5 - Prob. 50AYUCh. 10.5 - Prob. 51AYUCh. 10.5 - Prob. 52AYUCh. 10.5 - Prob. 53AYUCh. 10.5 - Prob. 54AYUCh. 10.5 - Prob. 55AYUCh. 10.5 - Prob. 56AYUCh. 10.5 - Prob. 57AYUCh. 10.5 - Prob. 58AYUCh. 10.5 - Prob. 59AYUCh. 10.5 - Prob. 60AYUCh. 10.6 - Prob. 1AYUCh. 10.6 - Prob. 2AYUCh. 10.6 - Prob. 3AYUCh. 10.6 - Prob. 4AYUCh. 10.6 - Prob. 5AYUCh. 10.6 - Prob. 6AYUCh. 10.6 - Prob. 7AYUCh. 10.6 - Prob. 8AYUCh. 10.6 - Prob. 9AYUCh. 10.6 - Prob. 10AYUCh. 10.6 - Prob. 11AYUCh. 10.6 - Prob. 12AYUCh. 10.6 - In Problems 13-24, analyze each equation and graph...Ch. 10.6 - In Problems 13-24, analyze each equation and graph...Ch. 10.6 - In Problems 13-24, analyze each equation and graph...Ch. 10.6 - 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Prob. 11AYUCh. 10.7 - Prob. 12AYUCh. 10.7 - Prob. 13AYUCh. 10.7 - Prob. 14AYUCh. 10.7 - Prob. 15AYUCh. 10.7 - Prob. 16AYUCh. 10.7 - Prob. 17AYUCh. 10.7 - Prob. 18AYUCh. 10.7 - In Problems 726, graph the plane curve whose...Ch. 10.7 - Prob. 20AYUCh. 10.7 - Prob. 21AYUCh. 10.7 - In Problems graph the plane curve whose parametric...Ch. 10.7 - In Problems graph the plane curve whose parametric...Ch. 10.7 - Prob. 24AYUCh. 10.7 - Prob. 25AYUCh. 10.7 - Prob. 26AYUCh. 10.7 - Prob. 27AYUCh. 10.7 - Prob. 28AYUCh. 10.7 - Prob. 29AYUCh. 10.7 - Prob. 30AYUCh. 10.7 - Prob. 31AYUCh. 10.7 - Prob. 32AYUCh. 10.7 - Prob. 33AYUCh. 10.7 - Prob. 34AYUCh. 10.7 - Prob. 35AYUCh. 10.7 - Prob. 36AYUCh. 10.7 - Prob. 37AYUCh. 10.7 - Prob. 38AYUCh. 10.7 - Prob. 39AYUCh. 10.7 - In Problems 39-42, find parametric equations for...Ch. 10.7 - Prob. 41AYUCh. 10.7 - Prob. 42AYUCh. 10.7 - Prob. 43AYUCh. 10.7 - Prob. 44AYUCh. 10.7 - In Problems 45-48, use a graphing utility to graph...Ch. 10.7 - Prob. 46AYUCh. 10.7 - Prob. 47AYUCh. 10.7 - Prob. 48AYUCh. 10.7 - Prob. 49AYUCh. 10.7 - Prob. 50AYUCh. 10.7 - Catching a Train Bill’s train leaves at 8:06 AM...Ch. 10.7 - Prob. 52AYUCh. 10.7 - Prob. 53AYUCh. 10.7 - Prob. 54AYUCh. 10.7 - Prob. 55AYUCh. 10.7 - Prob. 56AYUCh. 10.7 - Prob. 57AYUCh. 10.7 - Uniform Motion A Cessna (heading south at mph)...Ch. 10.7 - The Green Monster The left field wall at Fenway...Ch. 10.7 - Prob. 60AYUCh. 10.7 - Prob. 61AYUCh. 10.7 - Prob. 62AYUCh. 10.7 - Prob. 63AYUCh. 10.7 - Prob. 64AYUCh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Prob. 49RECh. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - Prob. 56RECh. 10 - Prob. 57RECh. 10 - Prob. 58RECh. 10 - Prob. 59RECh. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - Prob. 65RECh. 10 - Prob. 66RECh. 10 - Prob. 67RECh. 10 - Prob. 68RECh. 10 - Prob. 69RECh. 10 - Prob. 70RECh. 10 - Prob. 71RECh. 10 - Prob. 72RECh. 10 - Prob. 73RECh. 10 - Prob. 74RECh. 10 - Prob. 75RECh. 10 - Prob. 76RECh. 10 - Prob. 77RECh. 10 - Prob. 78RECh. 10 - Prob. 79RECh. 10 - Prob. 80RECh. 10 - Prob. 81RECh. 10 - Prob. 82RECh. 10 - Prob. 83RECh. 10 - Prob. 84RECh. 10 - In Problems 13, identify each equation. If it is a...Ch. 10 - In Problems 13, identify each equation. If it is a...Ch. 10 - In Problems identify each equation. If it is a...Ch. 10 - In Problems 46, find an equation of the conic...Ch. 10 - In Problems find an equation of the conic...Ch. 10 - In Problems find an equation of the conic...Ch. 10 - In Problems 79, identify each conic without...Ch. 10 - In Problems 79, identify each conic without...Ch. 10 - In Problems identify each conic without completing...Ch. 10 - Prob. 10CTCh. 10 - Prob. 11CTCh. 10 - Prob. 12CTCh. 10 - A parabolic reflector (paraboloid of revolution)...Ch. 10 - For find Ch. 10 - In the complex number system, solve the equation ...Ch. 10 - For what numbers x is 6xx2 ?Ch. 10 - Prob. 4CRCh. 10 - Prob. 5CRCh. 10 - Prob. 6CRCh. 10 - Prob. 7CRCh. 10 - Prob. 8CRCh. 10 - Prob. 9CRCh. 10 - Prob. 10CRCh. 10 - Solve the equation where. Ch. 10 - Find the rectangle equation of the plane curve...

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