Can anyone help me with this one asap? Thanks in advance.

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yradf57441

19.04.2021

Mathematics

$\frac{x^{2}}{144}+\frac{y^{2}}{79.995}=1$

Step-by-step explanation:

An ellipse centered a point (h,k) has the following formula:

$\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1$

The distance between foci is:

$2\cdot c = \sqrt{[8-(-8)]^{2}+(0-0)^{2}}$

$2\cdot c = 16$

c = 8

The center of the ellipse is:

C(x,y) = (-8 + 8, 0 + 0)

C(x,y) = (0,0)

The known vertex is on the horizontal axis of the ellipse. Then, the length of the semi-major axis is:

$a = \sqrt{(12-0)^{2}+(0-0)^{2}}$

a= 12

The length of the semi-minor axis is given by the following expression:

$c =\sqrt{a^{2}-b^{2}}$

$b = \sqrt{a^{2}-c^{2}}$

$b = \sqrt{12^{2}-8^{2}}$

$b \approx 8.944$

The equation of the ellipse is:

$\frac{x^{2}}{144}+\frac{y^{2}}{79.995}=1$

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