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Expert-verified Found in: Page 676 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # True or FalseThe equation $a{x}^{2}+6{y}^{2}-12y=0$ defines an ellipse if width="36" style="max-width: none; vertical-align: -5px;" $a>0$

The statement is true.

See the step by step solution

## Step 1. Given information

An equation is $a{x}^{2}+6{y}^{2}-12y=0$.

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

The ellipse is given by the equation given below.

$a{x}^{2}+6{y}^{2}-12y=0$

The ellipse is characterized by negative value of ${B}^{2}-4AC$.

$\begin{array}{rcl}{B}^{2}-4AC& =& {\left(0\right)}^{2}-4\left(a\right)\left(6\right)\\ & =& -24a\end{array}$

The range of $a$ can be determined for which the given equation is an ellipse.

$\begin{array}{rcl}{B}^{2}-4AC& <& 0\\ -24a& <& 0\\ a& >& 0\end{array}$

The given equation is an ellipse if for $a>0$, therefore the statement is True. ### Want to see more solutions like these? 