Math help!

Question

Write the ellipse equation if it contains the points A(0,-2), B(-6,2). I get an equation but I don't think it's right.

Answer 1

There's an infinite number of ellipses with those 2 points.

But the most simple equation would be found by using the two points as the left side and bottom of an ellipse.

Then the center is (0,2) Plug that into (x-h)^2/a^2 + (y-k)^2/b^2 = 1 to get

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

If x=0, then y= -2 and (-4)^2/b^2 = 1, so b = 4

If x=-6, then y=2 and (-6)^2/a^2 = 1, so a=6

the ellipse equation is

(x)^2/36 + (y-2)/16 = 1

But you could also have other elliptical equations that pass through the same 2 points.