The equation y2/100+x2/4 =1 represents an ellipse. which points are the vertices of the ellipse? (−10, 0) and (10, 0) (−2, 0) and (2, 0) (0, −10) and (0, 10) (0, −2) and (0, 2)

The vertices of the ellipse are the points (0 , -10) and (0 , 10) ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the standard equation of the ellipse

- The standard form of the equation of an ellipse

 with center (0 , 0 ) is x ²/a² + y²/b² = 1 , where  a > b

- The coordinates of the vertices are ( ± a , 0 )  

OR

- The standard form of the equation of an ellipse with  

   center (0 , 0) is x²/b² + y²/a² = 1 , where  a > b

- The coordinates of the vertices are (0 , ±a)

* Lets solve the problem

∵ The equation y²/100 + x²/4 = 1 represents an ellipse with center (0 , 0)

∵ √100 > √4

∵ a > b

∴ a must equal √100 and b must equal √4

∴ The standard form of the equation of the ellipse is x²/b² + y²/a² = 1

∴ The coordinates of the vertices are (0 , ± a)

* Lets find the vertices of the ellipse

∵ a = √100 = ± 10

∵ The coordinates of the vertices are (0 , ± a)

∵ a = ± 10

∴ The coordinates of the vertices are (0 , 10) , (0 , -10)

* The vertices of the ellipse are the points (0 , -10) and (0 , 10)

10 * 563.67 = 5636.7

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