Question

Without writing the equation 21x^2 - 84x + 12y^2 - 24y = -6 in the standard form, state whether the graph of this equation is a

parabola, circle, ellipse, or hyperbola.
a. parabola
c. hyperbola
b. ellipse
d. circle

Answer 1

b. ellipse

Explanation:

The squared terms have the same sign and different coefficients. That means the equation describes an ellipse.

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Additional comment

both variables are highest degree 2:

coefficients have the same sign and magnitude: circle

coefficients have the same sign and different magnitude: ellipse

coefficients have different signs: hyperbola*

only one variable has highest degree 2:

parabola

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* If the equation can be factored to a product of linear terms that is zero, then the equation is of two intersecting lines. This is a degenerate case of the hyperbola in which the major axis is zero: the two vertices are the same point.