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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

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ANSWER

[tex]\frac{ {x}^{2} }{64} + \frac{ {y}^{2} }{81} = 1[/tex]

EXPLANATION

The length of the vertical major axis is 18.

This implies that,

[tex]2a = 18.[/tex]

[tex]a = 9[/tex]

The length of the minor axis is 26.

This means that,

[tex]2b = 16[/tex]

[tex]b = 8[/tex]

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

[tex] \frac{ {x}^{2} }{ {b}^{2} } + \frac{ {y}^{2} }{ {a}^{2} } = 1[/tex]

[tex]\frac{ {x}^{2} }{ {8}^{2} } + \frac{ {y}^{2} }{ {9}^{2} } = 1[/tex]


[tex]\frac{ {x}^{2} }{64} + \frac{ {y}^{2} }{81} = 1[/tex]
zainebamir540

Answer:

x²/64+y²/81 = 1

Step-by-step 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.

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