Question

Write an equation for an ellipse centered at the origin, which has foci at (0,±55)(0,± 55)left parenthesis, 0, comma, plus minus, square root of, 55, end square root, right parenthesis and vertices at (0,±89)(0,± 89 )

Answer 1

Answer:

$\frac{x^{2} }{70^{2} } + \frac{y^{2} }{89^{2} } =1$

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:

$\frac{x^{2} }{b^{2} } + \frac{y^{2} }{a^{2} } =1$

replacing we have:

$\frac{x^{2} }{70^{2} } + \frac{y^{2} }{89^{2} } =1$