Q. 174E In the following exercises, iden... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 174E (page 1134)

In the following exercises, identify the type of graph.
$x = - y^{2} - 2 y + 3$
$9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$
$9 x^{2} + 25 y^{2} = 225$
$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$

Short Answer

Expert verified

$x = - y^{2} - 2 y + 3$ - Parabola
$9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$ - Hyperbola
$9 x^{2} + 25 y^{2} = 225$ - Circle
$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$ - Ellipse

Step by step solution

Step 1. Given information

The equations are

$x = - y^{2} - 2 y + 3$
role="math" localid="1646029866766" $9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$
role="math" localid="1646030038276" $9 x^{2} + 25 y^{2} = 225$
role="math" localid="1646030166290" $x^{2} + y^{2} - 4 x + 10 y - 7 = 0$

Identify the graph of the equation.

Step 2. Part a. Explanation

The equation is $x = - y^{2} - 2 y + 3$

Here, only one variable y is squared. so equation represent parabola.

Step 3. Part b. Explanation

The equation is $9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$

x²and y² terms have different signs, different coefficients, so the equation represents hyperbola.

Step 4. Part c. Explanation

The equation is $9 x^{2} + 25 y^{2} = 225$

x and y both terms are squared and have the same coefficients, So, the equation represents circle.

Step 5. Part d. Explanation

The equation is $x^{2} + y^{2} - 4 x + 10 y - 7 = 0$

x and y both the terms are squared and have the same sign, different coefficients, So the equation represents ellipse.

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91影视

In the following exercises, identify the type of graph.
$x = - y^{2} - 2 y + 3$
$9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$
$9 x^{2} + 25 y^{2} = 225$
$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Part a. Explanation

Step 3. Part b. Explanation

Step 4. Part c. Explanation

Step 5. Part d. Explanation

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91影视

In the following exercises, identify the type of graph.x=-y2-2y+39y2-x2+18y-4x-4=09x2+25y2=225x2+y2-4x+10y-7=0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Part a. Explanation

Step 3. Part b. Explanation

Step 4. Part c. Explanation

Step 5. Part d. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, identify the type of graph.
$x = - y^{2} - 2 y + 3$
$9 y^{2} - x^{2} + 18 y - 4 x - 4 = 0$
$9 x^{2} + 25 y^{2} = 225$
$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$