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General Equation of Parabola

If the point ...

Question

If the point $(1, 2, 3)$ is changes to the point $(2, 3, 1)$ through translation of axes, find the new origin.

(1, 1, 2)

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(1, - 1, 2)

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(- 1, - 1, 2)

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(1, 1, - 2)

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Solution

The correct option is D $(1, 1, - 2)$
$o r i g i n (0, 0, 0) \to (a, b, c) a f t e r T r a n s f o r m a t i o n o l d p o i n t (1, 2, 3) \to (2, 3, 1) a f t e r t r a n s f o r m a t i o n ∴ 2 = a + 1 ∴ a = 1 t h e n 3 = 2 + b s o b = 1 a n d 1 = 3 + c s o c = - 2 s o t h e n e w o r i g i n (1, 1, - 2)$

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