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The center of an ellipse is located at (0, 0). One focus is located at (12, 0), and one directrix is at x = 14 1/12.
what is the equation that represents the ellipse?????????

Respuesta :

The standard equation for an ellipse is
[tex] \frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} =1[/tex]
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes

Refer to the figure shown below.
The center of the ellipse is at (0,0). 
Therefore, h=0, k=0.

One focus is at (12, 0)
Therefore
c = 12

One directrix is at  14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13

Because c² = a² - b², obtain
b² = a² - c²
     = 169 - 144 = 25
b = 5

Answer:
The equation for the ellipse is
[tex] \frac{x^{2}}{169} + \frac{y^{2}}{25} =1[/tex]

Ver imagen Аноним
raphealnwobi

The equation of the ellipse is [tex]\frac{x^2}{169} + \frac{y^2}{25} =1[/tex]

Ellipse

The standard equation of an ellipse is:

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

Where (h, k) is the center, a is the major axis and b is the minor axis.

Given the focus at (12, 0), hence c = 12.

Directrix is at x = 14 1/12 = 169/12 = a² / c

hence a² = 169

c² = a² - b²

169 - b² = 12²

b² = 25

Hence the equation of the ellipse is [tex]\frac{x^2}{169} + \frac{y^2}{25} =1[/tex]

Find out more on Ellipse at: https://brainly.com/question/19507943

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