Find the standard form of the equation of the ellipse satisfying the given conditions.
Endpoints of major axis: $(3,12)$ and $(3,2)$
Endpoints of minor axis: $(5,7)$ and $(1,7)$

Step 1 ：The standard form of the equation of an ellipse is given by: \((x-h)^2/a^2 + (y-k)^2/b^2 = 1\) where \((h,k)\) is the center of the ellipse, \(a\) is the length of the semi-major axis, and \(b\) is the length of the semi-minor axis.

Step 2 ：The center of the ellipse is the midpoint of both the major and minor axes. The midpoint formula is given by: Midpoint = \([(x_1+x_2)/2 , (y_1+y_2)/2]\)

Step 3 ：So, the center of the ellipse \((h,k)\) is: \(h = (3+3)/2 = 3\) and \(k = (12+2)/2 = 7\)

Step 4 ：The length of the semi-major axis \(a\) is half the distance between the endpoints of the major axis. The distance formula is given by: Distance = \(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

Step 5 ：So, \(a = \sqrt{(3-3)^2 + (12-2)^2}/2 = \sqrt{0 + 100}/2 = 10/2 = 5\)

Step 6 ：The length of the semi-minor axis \(b\) is half the distance between the endpoints of the minor axis. So, \(b = \sqrt{(5-1)^2 + (7-7)^2}/2 = \sqrt{16 + 0}/2 = 4/2 = 2\)

Step 7 ：Substituting \(h = 3\), \(k = 7\), \(a = 5\), and \(b = 2\) into the standard form of the equation of an ellipse, we get: \((x-3)^2/5^2 + (y-7)^2/2^2 = 1\)

Step 8 ：Simplifying, we get: \((x-3)^2/25 + (y-7)^2/4 = 1\)

Step 9 ：This is the standard form of the equation of the ellipse. So, the final answer is \(\boxed{(x-3)^2/25 + (y-7)^2/4 = 1}\)