Chapter 11: Q. 175E (page 1134)

In the following exercises, identify the type of graph.
$x = - 2 y^{2} - 12 y - 16$
$x^{2} + y^{2} = 9$
$16 x^{2} - 4 y^{2} + 64 x - 24 y - 36 = 0$
$16 x^{2} + 36 y^{2} = 576$

Short Answer

Expert verified

$x = - 2 y^{2} - 12 y - 16$ - Parabola
$x^{2} + y^{2} = 9$ - Circle
$16 x^{2} - 4 y^{2} + 64 x - 24 y - 36 = 0$ - Hyperbola
$16 x^{2} + 36 y^{2} = 576$ - Ellipse

Step by step solution

. Given Information

The equations are

$x = - 2 y^{2} - 12 y - 16$
role="math" localid="1646031876856" $x^{2} + y^{2} = 9$
$16 x^{2} - 4 y^{2} + 64 x - 24 y - 36 = 0$
$16 x^{2} + 36 y^{2} = 576$

Identify the graph of the equation.

Step 2. Part a) Explanation

The equation is $x = - 2 y^{2} - 12 y - 16$

Here, only one variabley is squared. so equation represent parabola.

Step 3. Part b) Explanation

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

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

Step 4. Part c) Explanation

The equation is $16 x^{2} - 4 y^{2} + 64 x - 24 y - 36 = 0$

x²andy² terms have different signs, different coefficients, so the equation represents hyperbola.

Step 5. Part d) Explanation

The equation is $16 x^{2} + 36 y^{2} = 576$

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

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In the following exercises, identify the type of graph.
$x = - 2 y^{2} - 12 y - 16$
$x^{2} + y^{2} = 9$
$16 x^{2} - 4 y^{2} + 64 x - 24 y - 36 = 0$
$16 x^{2} + 36 y^{2} = 576$

Short Answer

Step by step solution

. 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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In the following exercises, identify the type of graph. x=-2y2-12y-16x2+y2=916x2-4y2+64x-24y-36=016x2+36y2=576

Short Answer

Step by step solution

. 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

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, identify the type of graph.
$x = - 2 y^{2} - 12 y - 16$
$x^{2} + y^{2} = 9$
$16 x^{2} - 4 y^{2} + 64 x - 24 y - 36 = 0$
$16 x^{2} + 36 y^{2} = 576$