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Show by implicit differentiation that the ellipse

$ \frac {x^2}{a^2} + \frac {y^2}{b^2} = 1 $

at the point $ ( x_o, y_o) $ is

$ \frac {x_o x}{a^2} + \frac {y_o y}{b^2} = 1 $

SEE PROOF

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