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

q63547wydf8Step-by-step explanation:...

Write an equation of the ellipse centered at the

reebz62

08.01.2022

1. $\dfrac{x^2}{36}+\dfrac{y^2}{25}=1.$

2. $\dfrac{x^2}{16}+\dfrac{y^2}{9}=1.$

Step-by-step explanation:

The equation of the ellipse is

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1.$

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

$\dfrac{x^2}{6^2}+\dfrac{y^2}{5^2}=1,$

$\dfrac{x^2}{36}+\dfrac{y^2}{25}=1.$

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

$\dfrac{x^2}{4^2}+\dfrac{y^2}{3^2}=1,$

$\dfrac{x^2}{16}+\dfrac{y^2}{9}=1.$

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