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.

Question

Shiksha Nation · Accepted 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.

Verified Answer