Answer:
[tex]\frac{x^{2} }{70^{2} } + \frac{y^{2} }{89^{2} } =1[/tex]
Step-by-step explanation:
Deducting by the value of the vertex, we can know that the ellipse has a vertical form, since in this case the vertex has the form (0, + -a)
the focus, we know it has the form (0, + -c)
We also know that b ^ 2 + c ^ 2 = a ^ 2
Therefore, we calculate b:
b ^ 2 = a ^ 2 - c ^ 2
replacing:
b ^ 2 = 89 ^ 2 - 55 ^ 2 = 4896
b = 69.97 = 70
Now, we know that the equation of a vertical ellipse is:
[tex]\frac{x^{2} }{b^{2} } + \frac{y^{2} }{a^{2} } =1[/tex]
replacing we have:
[tex]\frac{x^{2} }{70^{2} } + \frac{y^{2} }{89^{2} } =1[/tex]
