urielcastorena
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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)

Respuesta :

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

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