what if the center is located at (2,-3)? my major axis is 20 units long and minor axis is 8 units long.

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That depends on whether your major axis is the vertical axis or the horizontal one. Let's say that your 20 unit major axis is horizontal and the 8 unit minor axis is vertical. The basic form of the equation of your ellipse will be (x-2)^2/a^2 + (y+3)^2/b^2 = 1. Remember that the a-value is half the length of the horizontal axis (horizontal because it's below the x). The b-value is half the length of the vertical axis. So a = 20/2 = 10 and b = 8/2 = 4. Your ellipse has the equation (x-2)^2/10^2 + (y+3)^2/4^2 = 1. That simplifies to (x-2)^2/100 + (y+3)^2/16 = 1.