The point to which the origin should be shifted in order to eliminate x and y in the equation `2(x-5)^(2) + 3(y+7)^(2) =10` is

The point to which the origin should be shifted in order to eliminate x and y in the equation x^(2) + y^(2) + 8x - 6y + 25=0 is

The point to which the origin should be shifted in order to eliminate x and y terms in the equation 2x^(2) - 3y^(2) - 12x - 6y +5=0 is

The point to which the origin should be shifted in order to eliminate x and y terms in the equation x^(2)+3y^(2)-2x+12y+1=0 is

The point to which the origin should be shifted in order to eliminate x and y terms in the equation 4x^(2) + 9y^(2) - 8x + 36y +4=0 is

The point to which the origin should be shifted in order to eliminate x and y terms in the equation 4x^(2) + 9y^(2) - 8x + 36y +4=0 is

The point to which the origin should be shifted in order to eliminate x and y terms in the equation x^(2) + y^(2) - 2ax - 4ay + a^(2) = 0 is

The point to which the origin should be shifted in order to eliminate x and y in terms in the equation x^(2) -y^(2) + 2x + 4y=0 is

Statement - I : The point to which the origin has to be shifted to eliminate x and y term in the equation a(x + alpha)^(2) + b (y + beta)^(2) = c " is " (- alpha, - beta) Statement - II : The point to which the origin has to be shifted to eliminate x and y terms in ax^(2) + by^(2)+ 2gx + 2fy + c = 0 " is " ((-g)/(a),(-f)/(b)) Statement - III : If the axes are rotated through an angle 90^(0) then transformed equation of x^(2) - y^(2) = 1 " is " x^(2) - y^(2) = - 1 which of the above statements are true