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Answers without the blur. Sign up and see all textbooks for free! Q 13.

Expert-verified Found in: Page 677 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # In Problem, identify the graph of each equation without completing the squares.$6{x}^{2}+3{y}^{2}-12x+6y=0$

The equation represents graph of an ellipse.

See the step by step solution

## Step 1. Given information

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

## Step 2. Identify the graph.

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

(a) Defines a parabola if $AC=0$.

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

(c) Defines a hyperbola if $AC<0$

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

Since $AC>0$, the given equation is the equation of an ellipse. ### Want to see more solutions like these? 