How do you identity if the equation $x^{2} + 4 y^{2} + 2 x - 24 y + 33 = 0$ $x^2+4y^2+2x-24y+33=0$ is a parabola, circle, ellipse, or hyperbola and how do you graph it?

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How do you identity if the equation $x^{2} + 4 y^{2} + 2 x - 24 y + 33 = 0$ $x^2+4y^2+2x-24y+33=0$ is a parabola, circle, ellipse, or hyperbola and how do you graph it?

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Answer 1 · 2016-12-24T05:34:09

The given equation is ellipse.

Explanation:

Given -

$x^{2} + 4 y^{2} + 2 x - 24 y + 33 = 0$ $x^2+4y^2+2x-24y+33=0$

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

$a x^{2} + c y^{2} + d x + e y + f = 0$ $ax^2+cy^2+dx+ey+f=0$

The apply the following conditions to identify the equation.

If $a = c$ $a=c$ , It is a circle.
If $a \times c = 0$ $a xx c = 0$ , it is a parabola
If $a \times c > 0$ $a xx c > 0$ , it is ellipse .
If $a \times c < 0$ $a xx c< 0$ , it is a hyperbola

In our case

$a = 1; c = 4$ $a=1; c=4$

$1 \times 4 = 4 > 0$ $1 xx 4 = 4 >0$ , then the given equation is ellipse.

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How do you identity if the equation $x^{2} + 4 y^{2} + 2 x - 24 y + 33 = 0$ $x^2+4y^2+2x-24y+33=0$ is a parabola, circle, ellipse, or hyperbola and how do you graph it?

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Explanation:

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How do you identity if the equation $x^{2} + 4 y^{2} + 2 x - 24 y + 33 = 0$ $x^2+4y^2+2x-24y+33=0$ is a parabola, circle, ellipse, or hyperbola and how do you graph it?