Chapter 10: Q 8. (page 676)

True or False
The equation $a x^{2} + 6 y^{2} - 12 y = 0$ defines an ellipse if width="36">a>0

Short Answer

Expert verified

The statement is true.

Step by step solution

Step 1. Given information

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

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

The ellipse is given by the equation given below.

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

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

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

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

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

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

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True or False
The equation $a x^{2} + 6 y^{2} - 12 y = 0$ defines an ellipse if width="36">a>0

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

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

Discrete Mathematics

Calculus

Decision Maths

Mechanics Maths

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

True or False
The equation $a x^{2} + 6 y^{2} - 12 y = 0$ defines an ellipse if width="36">a>0