Chapter 10: Q 14. (page 677)

In Problem, identify the graph of each equation without completing the squares.
$2 x^{2} + y^{2} - 8 x + 4 y + 2 = 0$

Short Answer

Expert verified

An equation represents a graph of an ellipse.

Step by step solution

Step 1. Given information

An equation is $2 x^{2} + y^{2} - 8 x + 4 y + 2 = 0$ .

Step 2. Identify the graph.

The conic is given by the equation given below.

$2 x^{2} + y^{2} - 8 x + 4 y + 2 = 0$

The conic can be determined calculating the value of $B^{2} - 4 A C$ .

$\begin{array}{rcl} B^{2} - 4 A C & = & (0)^{2} - 4 (2) (1) \\ = & - 8 \end{array}$

The value of $B^{2} - 4 A C$ is negative and therefore the given conic is an ellipse since $A$ is not equal to $B$ .

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In Problem, identify the graph of each equation without completing the squares.
$2 x^{2} + y^{2} - 8 x + 4 y + 2 = 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify the graph.

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In Problem, identify the graph of each equation without completing the squares.2x2+y2-8x+4y+2=0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problem, identify the graph of each equation without completing the squares.
$2 x^{2} + y^{2} - 8 x + 4 y + 2 = 0$