Answer:
The correct option is 1.
Step-by-step explanation:
The standard form of an ellipse is
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex] .... (1)
Where, (h,k) is the center of ellipse, 2a is the width of the ellipse and 2b is height.
From the given figure it is clear that the center of the ellipse is (-1,2), the width of the ellipse is 4 and the height of the ellipse is 6.
[tex]h=-1,k=2[/tex]
[tex]2a=4\Rightarrow a=2[/tex]
[tex]2b=6\Rightarrow b=3[/tex]
Substitute h=-1, k=2, a=2 and b=3 in equation (1).
[tex]\frac{(x-(-1))^2}{2^2}+\frac{(y-2)^2}{3^2}[/tex]
[tex]\frac{(x+1)^2}{4}+\frac{(y-2)^2}{9}[/tex]
Therefore the correct option is 1.
