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Q 13.

Expert-verifiedFound in: Page 677

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.

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

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.

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