by transforming to parallel axes thru a chosen point (h,k).prove that the equation 12x^2-10xy+2y^2+11x-5y+2 can be reduced to an equation containning only second degree terms...

let x' =x-h and y'=y-k, 12(x-h)²+ 2(y-k)² -10(x-h)(y-k)+11(x-h) -5(y-k)+2

equating the coefficients of x and of y separately to zero we get

-24h+10k+11=0

-4k+10h-5=0

solving the above two simultaneous equations in h and k we get h=3/2 and k=5/2

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