Answer:
see explanation
Step-by-step explanation:
For the ellipse
[tex]\frac{x^2}{a^2}[/tex] + [tex]\frac{y^2}{b^2}[/tex] = 1
Then the vertices are (a, 0), (- a, 0) and (0, b), (0, - b)
Given
[tex]\frac{y^2}{100}[/tex] + [tex]\frac{x^2}{4}[/tex] = 1
Then
a² = 4 ⇒ a = 2 and b² = 100 ⇒ b = 10
Hence the vertices are
(2, 0), (- 2, 0) and (0, 10), (0, - 10)
The vertices of the ellipse are (2, 0), (0, -2), (10, 0), (0, -10).
Given that,
The equation represents an ellipse is,
[tex]\dfrac{y^2}{100} + \dfrac{x^2}{4} = 1[/tex]
We have to determine,
The points are the vertices of the ellipse.
According to the question,
The standard equation of the ellipse,
[tex]\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1[/tex]
And the vertices of an ellipse is (a, 0), (0, -a), (b, 0), (0, -b).
Convert the given equation in the form of the standard equation,
[tex]\dfrac{x^2}{2^2} + \dfrac{y^2}{10^2} = 1[/tex]
On comparing the given equation with the standard equation of an ellipse.
Then,
The value of a = 2 and b =10.
Therefore, the vertices of the ellipse are (2, 0), (0, -2), (10, 0), (0, -10).
To know more about Ellipse click the link given below.
https://brainly.com/question/14281133
