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

$$\mathrm{Given}\mathrm{an}\mathrm{Elipsis}\mathrm{in}(\mathrm{O};\overrightarrow{\mathrm{i}};\overrightarrow{\mathrm{j}})$$$$\left(\mathrm{E}\right):\frac{x^2}{1/4}+\frac{y^2}{1}=1.$$$$W\mathrm{e}\mathrm{admit}\mathrm{that}\mathrm{it}\mathrm{image}\mathrm{by}\mathrm{the}\mathrm{transformation}$$$$\mathrm{f}:\{\begin{array}{l}{x}^{\prime }=\sqrt{2}(x+y)\\ y^{\prime }=\sqrt{2}(-x+y)\end{array}$$$$isanelipsis\left(E^{\prime }\right):5x^2+5y^2+6xy-8=0$$$$$$$$\mathrm{Can}\mathrm{you}\mathrm{help}\mathrm{me}\mathrm{to}\mathrm{write}\mathrm{the}\mathrm{reduced}$$$$\mathrm{equation}\mathrm{of}\left({\mathrm{E}}^{\prime }\right)\mathrm{in}(\mathrm{O};\overrightarrow{\mathrm{i}};\overrightarrow{\mathrm{j}}).\mathrm{I}\mathrm{mean}$$$$\mathrm{in}\mathrm{the}\mathrm{similar}\mathrm{form}\mathrm{of}{\left(\mathrm{E}\right)}^{\prime }\mathrm{s}\mathrm{equation}.$$$$$$

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