Question

Please I need help Asap!!!!

Answer 1

`h = -3\\k = 3`

`a^2 = 25\\b^2 = 9`

`((x+3)^2)/(25) + ((y-3)^2)/(9) = 1`

Explanation:

The general equation of an ellipse is as follows:

`((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1`

Where the point (h, k) is the center of the circle

a is called semi major axis: horizontal distance from the ellipse to its center

b is the semi minor axis: vertical distance from the ellipse to its center.

See the attached image.

There you can notice that

`a = 5\\\\a^2 = 25\\\\b = 3\\\\b^2=9`

The center is at point (-3, 3)

Thus:

`h = -3\\k = 3`

Then the equation sought is:

`((x-(-3))^2)/(5^2) + ((y-3)^2)/(3^2) = 1`

Simplify

`((x+3)^2)/(5^2) + ((y-3)^2)/(3^2) = 1`