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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