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Answer 1 · 2017-12-19T12:31:57

$color(blue)(x^2/2+y^2/4 = 1)$

We are given the Equation of an Ellipse

$color(red)(4x^2+2y^2=8)$

For an Ellipse, the Standard Form is given by

$color(green)(x^2/a^2 + y^2/b^2 = 1)$ ... Equation.1

Using Algebra we can rewrite the equation in Standard Form

$(4x^2)/8+(2y^2)/8=8/8$

$color(blue)((x^2)/2+(y^2)/4=1)$ ... Equation.2

Additional points of interest:

By considering ... Equation.1 and ... Equation.2

we observe the following:

(I) $a^2 = 2^1$

(II) $b^2 = 2^2$

(III) $a < b$ and so, the Ellipse is vertical

(IV) Center of the Ellipse is $(0,0)$

Please analyze the graph attached for visual representation:

enter image source here