Q 3. - Precalculus Enhanced with Graphing Utilities

Question

True or False 

Every equation of the form

$x^2+y^2+ax+by+c=0$ has a circle as its graph.

Step-by-Step Solution

Answer

False

Step 1. Given information

An equation is $x^2+y^2+ax+by+c=0$.

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

Not all equations in the form of $x^2+y^2+ax+by+c=0$ 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.