Chapter 1: Q 3. (page 50)

True or False
Every equation of the form
$x^{2} + y^{2} + a x + b y + c = 0$ has a circle as its graph.

Short Answer

Expert verified

False

Step by step solution

Step 1. Given information

An equation is $x^{2} + y^{2} + a x + b y + c = 0$ .

Step 2. State whether the statement is true or false.

Not all equations in the form of $x^{2} + y^{2} + a x + b y + c = 0$ have a circle on its graph.

Cases where there is no solution for $x, y$ imply that there is no graph for the equation.

Example of this is when the sum of squares is negative.

example:

$\begin{array}{rcl} x^{2} + y^{2} + 8 & = & 0 \\ x^{2} + y^{2} & = & - 8 \end{array}$

So, the given statement is false.

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True or False
Every equation of the form
$x^{2} + y^{2} + a x + b y + c = 0$ has a circle as its graph.

Short Answer

Step by step solution

Step 1. Given information

Step 2. State whether the statement is true or false.

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True or FalseEvery equation of the formx2+y2+ax+by+c=0has a circle as its graph.

Short Answer

Step by step solution

Step 1. Given information

Step 2. State whether the statement is true or false.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

True or False
Every equation of the form
$x^{2} + y^{2} + a x + b y + c = 0$ has a circle as its graph.