Q.11.64TI Identify the graph of each equat... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q.11.64TI (page 1132)

Identify the graph of each equation as a circle, parabola, ellipse, or hyperbola.
$a) 16 x^{2} + 9 y^{2} = 144 b) y = 2 x^{2} + 4 x + 6 c) x^{2} + y^{2} + 2 x + 6 y + 9 = 0 d) 4 x^{2} - 16 y^{2} = 64$

Short Answer

Expert verified

$a) 16 x^{2} + 9 y^{2} = 144 G r a p h o f t h i s e q u a t i o n i s a n e l l i p s e . b) y = 2 x^{2} + 4 x + 6 T h e g r a p h f o r g i v e n e q u a t i o n i s p a r a b o l a c) x^{2} + y^{2} + 2 x + 6 y + 9 = 0 G r a p h o f t h e g i v e n e q u a t i o n i s c i r c l e d) 4 x^{2} - 16 y^{2} = 64 G r a p h o f t h e e q u a t i o n i s h y p e r b o l a$

Step by step solution

Part (a) Step 1. Given information

Given equation is $a) 16 x^{2} + 9 y^{2} = 144$

We have to identify the graph of the equation as the circle, ellipse, parabola, or hyperbola

Part (a) Step 2. Identifying the graph of the equation a) 16x2+9y2=144as a circle, parabola, ellipse, or hyperbola

According to the given equation $16 x^{2} + 9 y^{2} = 144$ .we can see that the terms x² and y² are the same sign but have different coefficients. so the graph of the given equation is an ellipse.

Part (b) Step 1. Given information

Given equation is

$y = 2 x^{2} + 4 x + 6$

We have to identify the graph of the equation as the circle, ellipse, parabola, or hyperbola

Part (b) Step 2. Identifying the graph of the equation

Here equation is $y = 2 x^{2} + 4 x + 6$ .

and one term is squared. so based on the graph this is a parabola equation.

Part (c) Step 1. Given information

Here given equation is $c) x^{2} + y^{2} + 2 x + 6 y + 9 = 0$

We have to match the graph of the equation as the circle, ellipse, parabola, or hyperbola

Part (c) Step 2. Identify the graph of the equation x2+y2+2x+6y+9=0 as a circle, hyperbola, ellipse, or parabola

The given equation is $x^{2} + y^{2} + 2 x + 6 y + 9 = 0$ .

Here we can notice that both terms of x²and y² have the same coefficients. so the graph of the equation is a circle.

Part (b) Step 1. Given information

Give equation is $d) 4 x^{2} - 16 y^{2} = 64$ .

We have to match the graph of the equation as the circle, ellipse, parabola, or hyperbola

Part (d ) Step2. Identify the equation 4x2-16y2=64 as a circle, hyperbola, ellipse, or parabola

Given equation is $4 x^{2} - 16 y^{2} = 64$ .

we can see that both terms of x² and y² have different signs and different coefficients, Thus the graph of the equation is hyperbola.

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91影视

Identify the graph of each equation as a circle, parabola, ellipse, or hyperbola.
$a) 16 x^{2} + 9 y^{2} = 144 b) y = 2 x^{2} + 4 x + 6 c) x^{2} + y^{2} + 2 x + 6 y + 9 = 0 d) 4 x^{2} - 16 y^{2} = 64$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Identifying the graph of the equation a) 16x2+9y2=144as a circle, parabola, ellipse, or hyperbola

Part (b) Step 1. Given information

Part (b) Step 2. Identifying the graph of the equation

Part (c) Step 1. Given information

Part (c) Step 2. Identify the graph of the equation x2+y2+2x+6y+9=0 as a circle, hyperbola, ellipse, or parabola

Part (b) Step 1. Given information

Part (d ) Step2. Identify the equation 4x2-16y2=64 as a circle, hyperbola, ellipse, or parabola

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91影视

Identify the graph of each equation as a circle, parabola, ellipse, or hyperbola.a)16x2+9y2=144b)y=2x2+4x+6c)x2+y2+2x+6y+9=0d)4x2-16y2=64

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Identifying the graph of the equation a) 16x2+9y2=144as a circle, parabola, ellipse, or hyperbola

Part (b) Step 1. Given information

Part (b) Step 2. Identifying the graph of the equation

Part (c) Step 1. Given information

Part (c) Step 2. Identify the graph of the equation x2+y2+2x+6y+9=0 as a circle, hyperbola, ellipse, or parabola

Part (b) Step 1. Given information

Part (d ) Step2. Identify the equation 4x2-16y2=64 as a circle, hyperbola, ellipse, or parabola

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Identify the graph of each equation as a circle, parabola, ellipse, or hyperbola.
$a) 16 x^{2} + 9 y^{2} = 144 b) y = 2 x^{2} + 4 x + 6 c) x^{2} + y^{2} + 2 x + 6 y + 9 = 0 d) 4 x^{2} - 16 y^{2} = 64$