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Question
Obtain the new equation 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
Solution
Let (X, Y) be the new coordinates of (x, y) when origin is shifted to the point O'(2, 2), axes remaining parallel.
∴ x = X + h and y = Y + k, where h = 2, k = 2
∴ x = X + 2 and y = Y + 2
Substituting the values of x, y in the equation
3x – y + 2 = 0, we get
3(X + 2) – (Y + 2) + 2 = 0
∴ 3X + 6 – Y – 2 + 2 = 0
∴ 3X – Y + 6 = 0
This is the new equation of the locus.
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