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Question
Class 11MathematicsStraight Lines

Find the point to which the origin should be shifted after shifting of origin so that the equation x² - 12x + 4 = 0 will have no first degree term. 

Verified Answer

Let origin be shifted to (h, k) and P(x, y) becomes P(X + h, Y + k).

Substituting in the given equation we get

(X + h)2 - 12(X + h) + 4 = 0

⇒ X2 + 2hX + h2 - 12X - 12h + 4 = 0

Since there is no first degree term: 2h - 12 = 0 ⇒ h = 6

Therefore, origin should be shifted to (6, k) for any real value k.

Find the point to which the origin should be shifted after shifting of origin so that the equation x² - 12x + 4 = 0 will have no first degree term.  | Shiksha Nation