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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:
y2 − 4x − 4y + 12 = 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
y2 – 4x – 4y + 12 = 0, we get,
(Y + 2)2 – 4(X + 2) – 4(Y + 2) + 12 = 0
∴ Y2 + 4Y + 4 – 4X – 8 – 4Y – 8 + 12 = 0
∴ Y2 – 4X = 0
This is the new equation of the locus.
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