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in Mathematics by (76.3k points)

Statement-1 : Through (λ, λ + 1) there cannot be more than one-normal to the parabola y2 = 4x if λ < 2. 

Statement-2 : The point (λ, λ + 1) lines out side the parabola for all λ ≠ 1. 

(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. 

(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1. 

(C) Statement – 1 is True, Statement – 2 is False. 

(D) Statement – 1 is False, Statement – 2 is True. 

1 Answer

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Best answer

Correct option: (b)

Explanation:

Any normal to the parabola y2 = 4x is y + tx = 2t + t3 

It this passes through (λ, λ + 1) 

⇒ t3 + t(2 - λ) - λ - 1 = 0 = f(t) say) λ < 2 than f′(t) = 3t2 + (2 - λ) > 0 

⇒ f(t) = 0 will have only one real root ⇒ A is true 

The statement-2 is also true since (λ+ 1)2 > 4λ is true for all λ ≠ 1. The statement-2 is true but does not follow true statement-2. 

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