Question

Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 16.

Answer 1

Let us assume then that the center is the origin.  If the major axis is 18, then a = 9 and a^2=81.  If the minor axis is 16, then b = 8 and b^2=64.  Now you can write the equation.  Remember that this ellipse is vertical and so a^2 goes under y^2

Answer 2

x²/64 + y²/81 = 1

Explanation:

Standard form of an equation for the ellipse is
`(x^(2) )/(a^(2))+(y^(2) )/(b^(2) )=1`

Here b is the length of vertical major axis = 9

and minor axis of length a = 8

Therefore the equation of the ellipse will be

`(x^(2) )/(8^(2) )+(y^(2) )/(9^(2) ) =1`

`(x^(2) )/(64)+(y^(2) )/(81)=1`

So the answer is x²/64 + y²/81 = 1