MATH SOLVE

5 months ago

Q:
# 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 = 1x squared divided by nine plus y squared divided by eight = 1x squared divided by eighty one plus y squared divided by sixty four = 1x squared divided by eight plus y squared divided by nine = 1

Accepted Solution

A:

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]

[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]