Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 10.

x^2/100 + y^2/256 = 1

Step-by-step explanation:

The standard form of an ellipse is (x-h) ^2/a^2 + (y-k) ^2/b^2=1

a is the horizontal radius

b is the vertical radius

h is the shift to the right

k is the shift upward

h and k will be shifts left and downward respectively if they are negative. Since the question doesn't mention any shifting we can just let them be 0 so everything is easier. The problem states the vertical axis is 16 and the horizontal axis is 10 so that means a = 10 and b = 16. Now we just plug in.

(x-h) ^2/a^2 + (y-k) ^2/b^2=1

a = 10

b = 16

h = 0

k = 0

x^2/10^2+y^2/16^2=1

x^2/100 + y^2/256 = 1