Question

Find the transformed equation of 2x² + 4xy + 5y² = 0 when the origin is shifted to (3, 4) by translation of axes.

Answer 1

Let (X, Y) be the new coordinates of the point (x, y).

=> x = X + 3, y = Y + 4

The transformed equation is 2(X + 3)² + 4(X + 3)(Y + 4) + 5(Y + 4)² = 0

=> 2(X² + 6X + 9) + 4(XY + 4X + 3Y +12) + 5(Y² + 8y + 16) = 0

=> 2X² + 12X + 18 + 4XY + 16X + 12Y + 48 + 5Y² + 40Y + 80 = 0

=> 2X² + 4XY + 5Y² + 28X + 52Y + 146 = 0