Question

Find the transformed equation of 4x² + 9y² – 8x + 36y + 4 = 0 when the axes are translated to the point (1, –2).

Answer 1

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

=> x = X + 1, y = Y – 2.

=> The transformed equation is 4(X + 1)² + 9(Y – 2)² – 8(X + 1) + 36(Y – 2) + 4 = 0.

=> 4(X² + 2X + 1) + 9(Y² – 4Y + 4) – 8X – 8 + 36Y – 72 + 4 = 0 => 4X² + 9Y² = 36.