Answer:
1. [tex]\dfrac{x^2}{1}+\dfrac{y^2}{4}=1.[/tex]
2. [tex]\dfrac{x^2}{121}+\dfrac{y^2}{100}=1.[/tex]
Step-by-step explanation:
The equation of the ellipse is
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\ (a>b)[/tex]
or
[tex]\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1\ (a<b).[/tex]
1. If the vertex of the ellipse is at point (0,2), then b=2.
If the co-vertex of the elllipse is at point (-1,0), then a=1.
The equation of the ellipse is
[tex]\dfrac{x^2}{1^2}+\dfrac{y^2}{2^2}=1,[/tex]
[tex]\dfrac{x^2}{1}+\dfrac{y^2}{4}=1.[/tex]
This ellipse has foci on y-axis.
2. If the vertex of the ellipse is at point (-11,0), then a=11.
If the co-vertex of the elllipse is at point (0,10), then b=10.
The equation of the ellipse is
[tex]\dfrac{x^2}{11^2}+\dfrac{y^2}{10^2}=1,[/tex]
[tex]\dfrac{x^2}{121}+\dfrac{y^2}{100}=1.[/tex]
