Suggested languages for you:

Americas

Europe

Q 8.

Expert-verifiedFound in: Page 676

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

True or False

The 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.

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

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.

94% of StudySmarter users get better grades.

Sign up for free