Find the equation in expanded form of the ellipse with center at (4,-2), a=2, b=3.

Thanks :]

To find the equation in expanded form of an ellipse, we can start with the equation of an ellipse in standard form:

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

where (h, k) is the center of the ellipse, and a and b are the lengths of the semi-major and semi-minor axes, respectively.

Given that the center of the ellipse is (4, -2) and the lengths of the semi-major and semi-minor axes are 2 and 3, respectively, we can substitute these values into the standard form equation.

Thus, we have:

(x-4)^2/2^2 + (y+2)^2/3^2 = 1

Simplifying further, we get:

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

Hence, the equation in expanded form of the ellipse with the given values is:

9(x-4)^2 + 4(y+2)^2 = 36