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is the graph a parabola, circle, ellipse, or hyperbola?
x^2 +4y^2+2x-24y+33=0

The given equation is ellipse.

Step-by-step explanation:

Given : -

x² + 4y² + 2x - 24y + 33 = 0

Conic section formula, in the general form, could be written like this -

ax² + cy² +dx + ey + f = 0

The apply the following conditions to identify the equation.

If a = c, It is a circle.

If a x c = 0, It is a parabola.

If a x c > 0, It is a ellipse .

If a x c < 0,It is a  hyperbola.

In this case:

a = 1;c = 4

1 x 4 = 4 > 0, then the given equation is ellipse.

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step-by-step explanation:

apex answer