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Write an equation of the ellipse centered at the origin given its vertex and co vertex ps can plz do both

Write an equation of the ellipse centered at the origin given its vertex and co vertex-example-1

1 Answer

3 votes

Answer:

1.
(x^2)/(36)+(y^2)/(25)=1.

2.
(x^2)/(16)+(y^2)/(9)=1.

Explanation:

The equation of the ellipse is


(x^2)/(a^2)+(y^2)/(b^2)=1.

1. If the vertex of the ellipse is at point (6,0), then a=6.

If the co-vertex of the elllipse is at point (0,-5), then b=5.

The equation of the ellipse is


(x^2)/(6^2)+(y^2)/(5^2)=1,


(x^2)/(36)+(y^2)/(25)=1.

2. If the vertex of the ellipse is at point (4,0), then a=4.

If the co-vertex of the elllipse is at point (0,3), then b=3.

The equation of the ellipse is


(x^2)/(4^2)+(y^2)/(3^2)=1,


(x^2)/(16)+(y^2)/(9)=1.

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