Question

Write the equation of the ellipse shown in the graph

Answer 1

A. (x+1)^2/4 + (y-2)^2/9=1

Answer 2

The correct option is 1.

Explanation:

The standard form of an ellipse is

`((x-h)^2)/(a^2)+((y-k)^2)/(b^2)` .... (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.

`h=-1,k=2`

`2a=4\Rightarrow a=2`

`2b=6\Rightarrow b=3`

Substitute h=-1, k=2, a=2 and b=3 in equation (1).

`((x-(-1))^2)/(2^2)+((y-2)^2)/(3^2)`

`((x+1)^2)/(4)+((y-2)^2)/(9)`

Therefore the correct option is 1.