Respuesta :

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The equation of a circle is:

(x - h)² + (y - k)² = r²

The equation of a parabola is:

(x - h)² = 4p(y - k)

The equation of an ellipse is: 

[tex] \frac{(x-h) ^{2} }{ a^{2} } + \frac{(y-k) ^{2} }{ b^{2} } = 1[/tex]

where variables a and b and the two different measurements of the vertices

The equation of a hyperbola is: 

[tex] \frac{((x-h)^{2} }{ a^{2} } - \frac{(y-k)^{2} }{ b^{2} } = 1[/tex] if it is with a horizontal transverse axis

[tex] \frac{ (y-k)^{2} }{ b^{2} } - \frac{ (x-h)^{2} }{ a^{2} } = 1[/tex] if it is with a vertical transverse axis

Notice these have a subtraction operation, the exact opposite ellipse. 

Answer:

Step-by-step explanation:

The general form of a conic section:

Ax^2+Bxy+Cy^2+Dx+Ey+F=0

If B = 0, then:

Ellipse: x² and y² have different positive coefficients.

Hyperbola: x² and y² have different signs.

Otherwise, determine the discriminant:

If B² − 4AC < 0, then the conic is an ellipse.

If B² − 4AC > 0, then the conic is a hyperbola.