2.- Find the equation of the ellipse whose foci are F(0, 3/2) and F'(0, - 3/2) and such that the sum of the distances of the points on it to the foci is 5, in Spanish

Step 1:
Let the coordinates of the center of the ellipse be (h, k).
The distances from the center to the foci are c and -c, respectively, where c is the distance between the center and one of the foci.
Since the sum of the distances from any point on the ellipse to the foci is given as 5, we have:
2a = 5

Step 2:
The distance between the foci is 2c = 3.
So, we have:
a = \frac{5}{2}
c = \frac{3}{2}

Step 3:
The equation of an ellipse centered at (h, k) with major axis along y-axis is:
\frac{(y-k)^2}{b^2} + \frac{(x-h)^2}{a^2} = 1
where a and b are the semi-major and semi-minor axes lengths, respectively.

Step 4:
Substitute the values of a, c, h, and k into the equation:
\frac{(y-k)^2}{\left(\frac{b}{2}\right)^2} + \frac{(x-h)^2}{\left(\frac{5}{2}\right)^2} = 1
\frac{(y-k)^2}{\left(\frac{b}{2}\right)^2} + \frac{x^2}{\left(\frac{5}{2}\right)^2} = 1
\frac{(y-k)^2}{\left(\frac{b}{2}\right)^2} + \frac{x^2}{\frac{25}{4}} = 1

Step 5:
Comparing the equation of the ellipse with the standard form, we get:
b = 2
k = 0

So, the equation of the ellipse is:
\frac{y^2}{4} + \frac{4x^2}{25} = 1

\boxed{\frac{y^2}{4} + \frac{4x^2}{25} = 1}