The point to which the origin is to be shifted to remove the first degree terms from the equation 2 x^2+4 x y-6 y^2+2 x+8 y+1=0 is

Step-by-step solution

2 x^2+4 x y-6 y^2+2 x+8 y+1=0 is in the form of aligned & a x^2+2 h x y+b y^2+2 g x+2 f y+c=0, we get & a=2, h=2, b=-6, g=1, f=4, c=1 aligned Required point aligned & = ( b g-f h h^2-a b , a f-g h h^2-a b )= ( -6-8 4+12 , 8-2 4+12 ) & = ( -14 16 , 6 16 )= ( -7 8 , 3 8 ) aligned