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Which of the following is the equation of an ellipse centered at (5,1) having a vertical minor axis of length 4 and a major axis of length 6?

Options are in image

Which of the following is the equation of an ellipse centered at 51 having a vertical minor axis of length 4 and a major axis of length 6 Options are in image class=

Respuesta :

AlexVavvas

Answer:

D

Step-by-step explanation:

Any ellipse has the following equ

ation:

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

where

  • 2b = vertical axis length
  • 2a = horizontal axis length

(as in the picture)

So it should be like:

[tex] \frac{ {x}^{2} }{ { (\frac{6}{2} )}^{2} } + \frac{ {y}^{2} }{ {( \frac{4}{2} )}^{2} } = 1 \\ \frac{ {x}^{2} }{ 9} + \frac{ {y}^{2} }{ 4 } = 1[/tex]

Since it should be moved to the right and up, the answer would be:

[tex]\frac{ {(x - 5)}^{2} }{ 9} + \frac{ {(y - 1)}^{2} }{ 4 } = 1[/tex]

Ver imagen AlexVavvas
nutanraj654

Option D. (x - 5)²/9 + ( y - 1 )²/4 = 1

An ellipse has the following equation:

x²/a² + y²/ b² = 1

where

2b = vertical axis length

2a = horizontal axis length

So it should be like:

x²/(6÷2)² + y²/ (4÷2)² = 1

x²/9 + y²/4 = 1

Since it should be moved to the right and up, the answer would be:

(x - 5)²/9 + ( y - 1 )²/4 = 1

Please check the attached diagram for more details.

Learn more about the equation at

https://brainly.com/question/1214333

#SPJ2

Ver imagen nutanraj654