Find the standard form of the equation of the ellipse satisfying the following conditions. Vertices of major axis are $(-2,12)$ and $(-2,2)$ The length of the minor axis is 8 .

Step 1 ：Given that the vertices of the major axis are $(-2,12)$ and $(-2,2)$, we can find the center of the ellipse by finding the midpoint of these two points. The length of the major axis is the distance between these two points, so $2a$ is the distance between $(-2,12)$ and $(-2,2)$.

Step 2 ：The length of the minor axis is given as 8, so $2b = 8$.

Step 3 ：The standard form of the equation of an ellipse with its center at $(h, k)$, major axis of length $2a$ along the y-axis, and minor axis of length $2b$ along the x-axis is given by: \[\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1\]

Step 4 ：Now that we have the center of the ellipse $(h, k)$ and the lengths of the semi-major and semi-minor axes $a$ and $b$, we can substitute these values into the standard form of the equation of an ellipse to get the equation of the ellipse satisfying the given conditions.

Step 5 ：Final Answer: The standard form of the equation of the ellipse satisfying the given conditions is \[\boxed{\frac{(x+2)^2}{16} + \frac{(y-7)^2}{25} = 1}\]