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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 10: Q 20. (page 677)

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

Short Answer

Expert verified

The graph is of a circle.

Step by step solution

01

Step 1. Given information

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

02

Step 2. Identify the graph.

Consider the equation $2 x^{2} + 2 y^{2} - 8 x + 8 y = 0$ .

Compare this equation with equation $A x^{2} + C y^{2} + D x + E y + F = 0$ .

$\begin{array}{rcl} A & = & 2 \\ C & = & 2 \\ A C & = & 2 (2) \\ = & 4 \\ > & 0 \end{array}$

So, the equation represents a circle.

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In Problem, identify the graph of each equation without completing the squares.

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