Question

Obtain the new equations of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same: x² + y² – 3x = 7

Answer 1

Given, (h, k) = (2, 2)
Let (X, Y) be the new co-ordinates of the point (x, y).
∴ x = X + h and y = Y + k
∴ x = X + 2 and y = Y + 2
Substituting the values of x and y in the equation x² + y² – 3x = 7, we get
(X + 2)² + (Y + 2)² – 3(X + 2) = 7
∴ X² + 4X + 4 + Y² + 4Y + 4 – 3X – 6 = 7
∴ X² + Y² + X + 4Y – 5 = 0, which is the new equation of locus.