Answer:
1. [tex]\dfrac{x^2}{36}+\dfrac{y^2}{25}=1.[/tex]
2. [tex]\dfrac{x^2}{16}+\dfrac{y^2}{9}=1.[/tex]
Step-by-step explanation:
The equation of the ellipse is
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1.[/tex]
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
[tex]\dfrac{x^2}{6^2}+\dfrac{y^2}{5^2}=1,[/tex]
[tex]\dfrac{x^2}{36}+\dfrac{y^2}{25}=1.[/tex]
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
[tex]\dfrac{x^2}{4^2}+\dfrac{y^2}{3^2}=1,[/tex]
[tex]\dfrac{x^2}{16}+\dfrac{y^2}{9}=1.[/tex]
