Answer:
The answer is below
Step-by-step explanation:
The standard form of the equation of an ellipse with major axis on the y axis is given as:
[tex]\frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1[/tex]
Where (h, k) is the center of the ellipse, (h, k ± a) is the major axis, (h ± b, k) is the minor axis, (h, k ± c) is the foci and c² = a² - b²
Since the minor axis is at (37,0) and (-37,0), hence k = 0, h = 0 and b = 37
Also, the foci is at (0,5) and (0, -5), therefore c = 5
Using c² = a² - b²:
5² = a² - 37²
a² = 37² + 5² = 1369 + 25
a² = 1394
Therefore the equation of the ellipse is:
[tex]\frac{x^2}{1369}+ \frac{y^2}{1394} =1[/tex]
