Question

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

Answer 1

Answer:

$\dfrac{x^2}{49}+\dfrac{y^2}{25}=1.$

Step-by-step explanation:

The equation of the ellipse is

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

If the vertex of the ellipse is at point (-7,0), then a=7.

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

The equation of the ellipse is

$\dfrac{x^2}{7^2}+\dfrac{y^2}{5^2}=1,$

$\dfrac{x^2}{49}+\dfrac{y^2}{25}=1.$