Answer:
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)
