Chapter 10: Q 13. (page 677)

In Problem, identify the graph of each equation without completing the squares.
$6 x^{2} + 3 y^{2} - 12 x + 6 y = 0$

Short Answer

Expert verified

The equation represents graph of an ellipse.

Step by step solution

Step 1. Given information

An equation is $6 x^{2} + 3 y^{2} - 12 x + 6 y = 0$ .

Step 2. Identify the graph.

The equation $A x^{2} + C y^{2} + D x + E y + F = 0$ where $A$ and $C$ both cannot be zero,

(a) Defines a parabola if $A C = 0$ .

(b) Defines an ellipse (or a circle) if $A C > 0$ .

Comparing the given equation with the equation $A x^{2} + C y^{2} + D x + E y + F = 0$ we can see that $A = 6$ and $C = 3$ So, we get $A C = 18$ .

Since $A C > 0$ , the given equation is the equation of an ellipse.

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In Problem, identify the graph of each equation without completing the squares.
$6 x^{2} + 3 y^{2} - 12 x + 6 y = 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify the graph.

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In Problem, identify the graph of each equation without completing the squares.6x2+3y2-12x+6y=0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Logic and Functions

Mechanics Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

In Problem, identify the graph of each equation without completing the squares.
$6 x^{2} + 3 y^{2} - 12 x + 6 y = 0$