Without changing the direction of coordinates axes, origin is transferred to (α,β)so that the linear terms in the equation x2 + y2 + 2x – 4y + 6 = 0 are eliminated. The point (α,β) is

The given equation isx2 + y2 + 2x – 4y + 6 = 0                                          (1)Putting x = x′ + α, y = y′ + β in (1), we getx′2 + y′2 + x′(2α+ 2) + y′(2β – 4) + (α2 + β 2 + 2α – 4β+ 6) = 0To eliminate linear terms, we should have 2α + 2 = 0 and 2β– 4 = 0⇒ α = –1 and β = 2∴(α, β) ≡ (–1, 2)