The coordinates of the point where origin to be shifted so that the equation y2+4y+8x−2=0 will not contain the term in y and the constant term, are

Let the origin be shifted to (h, k). Then, x=X+k and y=Y+k. Substituting x=X+h, y=Y+k in the equationy2+4y+8x−2=0, we get(Y+k)2+4(Y+k)+8(X+h)−2=0=Y2+(4+2k)Y+8X+k2+4k+8h−2=0For this equation to be free from the term containing Y and the constant term, we rnust have4+2k=0 and k2+4k+8h−2=0⇒k=−2a and h=34.Hence, the origin must be shifted at the point ( 3/ 4, - 2).