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Question Number 140708 by mathocean1 last updated on 11/May/21

Given an Elipsis in (O; \vec{i}; \vec{j})

(E) : \frac{x^{2}}{1 / 4} + \frac{y^{2}}{1} = 1 .

W e admit that it image by the transformation

f : {\begin{cases} x^{'} = \sqrt{2} (x + y) \\ y^{'} = \sqrt{2} (- x + y) \end{cases}

i s a n e l i p s i s (E^{'}) : 5 x^{2} + 5 y^{2} + 6 x y - 8 = 0

Can you help me to write the reduced

equation of (E^{'}) in (O; \vec{i}; \vec{j}) . I mean

in the similar form of {(E)}^{'} s equation .