Given equation: y2−8x+6y+1=0 ⇒y2+6y+9−9−8x+1=0 ⇒(y+3)2−8x−8=0 ⇒(y+3)2=8x+8 ⇒(y+3)2=8(x+1) Let new coordinate axes be X and Y Here X=x+1 and Y=y+3 ⇒Y2=4aX Now comparing with above equation, ∴4a=8⇒a=2 Focus: (a, 0) X = a and Y = 0 ⇒ x + 1 = 2 and y + 3 = 0 ⇒ x = 1 and y = -3 ∴ focus of parabola is (1, -3)