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Answer 1 · 2017-01-31T18:34:58

#"Centre is "(1,1)," and, Eccentricity "e=1/2#.

Shifting the Origin to the point #(1,1)#, suppose that, old co-ords.

#(x,y)" becomes new ones "(X,Y)"#.

Therefore, #x=X+1, y=Y+1.#

Substituting in the given eqn., it becomes, #8X^2+6Y^2=1, i.e.,#

#X^2/(1/8)+y^2/(1/6)=1#.

Comparing with the Standard Eqn. of Ellipse# : X^2/a^2+Y^2/b^2=1#,

#a^2=1/8, b^2=1/6 :. b^2>a^2#. Then, the Eccentricity #e# is given by,

#a^2=b^2(1-e^2) :. e^2=1-a^2/b^2=1-(1/8)/(1/6)=1-6/8=1/4#

#:. e=1/2#

The Centre is #(X,Y)=(0,0) rArr (x-1,y-1)=(0,0), i.e.,#

#" Centre "(1,1)#.

Enjoy Maths.!