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

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b