Answer:
[tex]\frac{x^{2}}{144}+\frac{y^{2}}{79.995}=1[/tex]
Step-by-step explanation:
An ellipse centered a point (h,k) has the following formula:
[tex]\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1[/tex]
The distance between foci is:
[tex]2\cdot c = \sqrt{[8-(-8)]^{2}+(0-0)^{2}}[/tex]
[tex]2\cdot c = 16[/tex]
[tex]c = 8[/tex]
The center of the ellipse is:
[tex]C(x,y) = (-8 + 8, 0 + 0)[/tex]
[tex]C(x,y) = (0,0)[/tex]
The known vertex is on the horizontal axis of the ellipse. Then, the length of the semi-major axis is:
[tex]a = \sqrt{(12-0)^{2}+(0-0)^{2}}[/tex]
[tex]a= 12[/tex]
The length of the semi-minor axis is given by the following expression:
[tex]c =\sqrt{a^{2}-b^{2}}[/tex]
[tex]b = \sqrt{a^{2}-c^{2}}[/tex]
[tex]b = \sqrt{12^{2}-8^{2}}[/tex]
[tex]b \approx 8.944[/tex]
The equation of the ellipse is:
[tex]\frac{x^{2}}{144}+\frac{y^{2}}{79.995}=1[/tex]
