state what type of conic section graph is made by 21x^2-84x+12y^2-24y=-6

You can use the following test to identify the conic.

No: It's a parabola.

Yes: Go to the next test....

Yes: It's an hyperbola.

No: Go to the next test....

Yes: It's a circle.

No: It's an ellipse.

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Both the variables are squared. So it is not a parabola.

The squared terms which are 21x^2 and 12y^2 do not have opposite signs. So it is not a hyperbola.

The square terms are not multiplied by the same number.

So it is an ellipse.

ANSWER: Ellipse

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