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Question

If (α2,α2) be a point interior to the regions of the parabola y2=2x bounded by the chord joining the points (2,2) and (8,4), then α belongs to the interval


Correct Answer
A
2+22<α<2
Your Answer
B
α>2+22
Your Answer
C
α>222
Your Answer
D
α<222

Solution

The correct option is A 2+22<α<2
Chord joining point (2,2) and (8,4) is 
y2=66(x2)
y2=x+2
y+x4=0


For (α2,α2) to lie inside the parabola,
(α2)22(α2)<0
α2+4α4>0
α(,222)(2+22,)     (1)

Now for chord, (0,0) and (α2,α2) should lie on same side of origin.
y+x4=0 
0+04<0
and α2+α6<0
(α+3)(α2)<0α(3,2)     (2)

From (1) and (2), we get
α(2+22,2)

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