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Chapter 10: Q 8. (page 676)

True or False

The equation ax2+6y2-12y=0defines an ellipse if width="36">a>0

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Step 1. Given information

An equation isax2+6y2-12y=0.

02

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

The ellipse is given by the equation given below.

ax2+6y2-12y=0

The ellipse is characterized by negative value of B2-4AC.

B2-4AC=(0)2-4(a)(6)=-24a

The range of acan be determined for which the given equation is an ellipse.

B2-4AC<0-24a<0a>0

The given equation is an ellipse if for a>0, therefore the statement is True.

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