Find an equation in standard form for the ellipse with vertical major axis of length 18 and minor axis length of 6

The equation of the ellipse is standard form is expressed as:

x²/81 + y²/9 = 1

Step-by-step explanation:

General equation of an ellipse is expressed as shown below:

x²/a² + y²/b² = 1

Length of the major axis = 2a

Length of the Minor axis = 2b

Given length of major axis = 18

18 = 2a

a = 9

Similarly, if the length of the minor axis is 6, then

6 = 2b

b = 3

The equation of the ellipse becomes;

x²/9² + y²/3² = 1

x²/81 + y²/9 = 1

Finding the LCM

(x²+9y²) / 81 = 1

x²+9y² = 81