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 (2, 0), (0, -2), (10, 0), (0, -10).

Given that,

The equation represents an ellipse is,

We have to determine,

The points are the vertices of the ellipse.

According to the question,

The standard equation of the ellipse,

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,

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.

link

see explanation

Step-by-step explanation:

For the ellipse

+ = 1

Then the vertices are (a, 0), (- a, 0) and (0, b), (0, - b)

Given

+ = 1

Then

a² = 4 ⇒ a = 2 and b² = 100 ⇒ b = 10

Hence the vertices are

(2, 0), (- 2, 0) and (0, 10), (0, - 10)