Question

Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 16. (2 points)

x squared divided by sixty four plus y squared divided by eighty one = 1

x squared divided by nine plus y squared divided by eight = 1

x squared divided by eighty one plus y squared divided by sixty four = 1

x squared divided by eight plus y squared divided by nine = 1

Answer 1

x²/64+y²/81 = 1

Explanation:

We have given the the vertical major axis of ellipse= 18

And minor axis of length 16.

We have to find the equation of ellipse .

The standard equation of ellipse is:

x²/d² +y²/c² = 1 when orientation is y -axis.

As vertical major axis of ellipse= 18

So, 2c = 18 then c = 9

And minor axis of length = 16.

So, 2d = 16

d = 8

Put the values in standard equation we get,

x²/64+y²/81 = 1 is the equation of ellipse.

Answer 2

ANSWER


`\frac{ {x}^(2) }{64} + \frac{ {y}^(2) }{81} = 1`

EXPLANATION

The length of the vertical major axis is 18.

This implies that,


`2a = 18.`


`a = 9`

The length of the minor axis is 26.

This means that,


`2b = 16`


`b = 8`

The orientation is on the y-axis. The equation is given by:


`\frac{ {x}^(2) }{ {b}^(2) } + \frac{ {y}^(2) }{ {a}^(2) } = 1`


`\frac{ {x}^(2) }{ {8}^(2) } + \frac{ {y}^(2) }{ {9}^(2) } = 1`



`\frac{ {x}^(2) }{64} + \frac{ {y}^(2) }{81} = 1`