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If L ≡ x + y – 1 = 0 is a line and S ≡ y – x + x2 = 0 is a parabola, then which of the following is true?
(A) L = 0 and S = 0 do not have common points
(B) L = 0 cuts S = 0 in two distinct points
(C) L = 0 touches the parabola S = 0
(D) L = 0 is the directrix of the parabola S = 0
If L ≡ x + y – 1 = 0 is a line and S ≡ y – x + x2 = 0 is a parabola, then which of the following is true?
(A) L = 0 and S = 0 do not have common points
(B) L = 0 cuts S = 0 in two distinct points
(C) L = 0 touches the parabola S = 0
(D) L = 0 is the directrix of the parabola S = 0
Correct option (C) L = 0 touches the parabola S = 0
Explanation :
Substituting y = 1 x in the equation of the parabola, we get
1 – x – x + x2 = 0
⇒ x2 – 2x + 1 = 0
⇒ (x – 1)2 = 0
Hence, L = 0 touches the parabola at (1, 1).