Transformation of axes (translation)
Two-dimensional geometry · Mathematics
Study notes
Q: Shift origin to (2,−1). Find the new equation of x² + y² − 4x + 2y − 4 = 0. Substitute x = X+2, y = Y−1: (X+2)² + (Y−1)² − 4(X+2) + 2(Y−1) − 4 = 0 X²+4X+4 + Y²−2Y+1 −4X−8 +2Y−2 −4 = 0 X² + Y² − 9 = 0. Linear terms gone!