If you have four points $A(4,10),\; B(-4,10),\; C(-4,-10),\; D(4,-10)$ and an ellipse passes $A,B,C$ and $D$ points and these points form a rectangle inside this ellipse.
How to find the equation of that ellipse?
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1The general equation of an ellipse is $$(x-x_0)^2/a^2+(y-y_0)^2/b^2=1$$ – Yuriy S Nov 01 '18 at 15:54
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There's not a unique solution. The circle of radius $\sqrt{4^2+10^2}$ passes through those points. – B. Goddard Nov 01 '18 at 16:00
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$(\frac {x}{4})^2 + (\frac {y}{10})^2 = 2$ is an equation that will work. – Doug M Nov 01 '18 at 16:02
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@DougM How did you find that b=2 ? – Ahmad Sadoun Shakir Nov 01 '18 at 16:05
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Four points are not enough to determine a unique ellipse. Even if you require that it be in standard position, they don’t provide enough constraints due to the symmetries among them. – amd Nov 01 '18 at 19:20
