Let A (0, 2), B and C are points on parabola y2=x+4 and such that CBA=π2 , then the range of ordinate of C is

A(0, 2),B=(t12−4,t1)C=(t2−4, t) 2−t14−t12.t1−tt12−t2=−1⇒12+t1.1t+t1=−1 ⇒t12+(2+t)t1+(2t+1)=0 For real t1 , ⇒(2+t)2−4(2t+1)=0 ⇒t2−4t≥0⇒t∈(−∞, 0] ∪[4, ∞)

Let A (0, 2), B and C are points on parabola y2=x+4 and such that CBA=π2 , then the range of ordinate of C is

A(0, 2),B=(t12−4,t1)C=(t2−4, t) 2−t14−t12.t1−tt12−t2=−1⇒12+t1.1t+t1=−1 ⇒t12+(2+t)t1+(2t+1)=0 For real t1 , ⇒(2+t)2−4(2t+1)=0 ⇒t2−4t≥0⇒t∈(−∞, 0] ∪[4, ∞)

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Let A (0, 2), B and C are points on parabola $y^{2} = x + 4$ and such that $C B A = \frac{π}{2}$ , then the range of ordinate of $C$ is

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$(- \infty, 0) \cup (4, \infty)$

$(- \infty, 0] \cup [4, \infty)$

$[0, 4]$

$(- \infty, 0) \cup [4, \infty)$

answer is B.

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Detailed Solution

$A (0, 2), B = (t_{1}^{2} - 4, t_{1}) C = (t^{2} - 4, t) \frac{2 - t_{1}}{4 - t_{1}^{2}} . \frac{t_{1} - t}{t_{1}^{2} - t^{2}} = - 1 \Rightarrow \frac{1}{2 + t_{1}} . \frac{1}{t + t_{1}} = - 1 \Rightarrow t_{1}^{2} + (2 + t) t_{1} + (2 t + 1) = 0$