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: 3x – y + 2 = 0

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 3x – y + 2 = 0, we get
3(X + 2) – (Y + 2) + 2 = 0
∴ 3 X + 6 – Y – 2 + 2 = 0
∴ 3 X – Y + 6 = 0, which is the new equation of locus.