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Question

If (α+1,α) be a point interior to the regions of the parabola y2=4x bounded by the chord joining the points (6,5) and (7,4), then the total number of integral values of α is

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Solution

For (α+1,α) to lie inside the parabola,
α24(α+1)<0
α(222,2+22) (1)

Equation of chord passing through (6,5) and (7,4) is x+y=11
(0,0) and (α+1,α) should lie on the same side.
0+011<0,
α+1+α11<0
α<5 (2)



By (1) and (2),
α(222,2+22)
Integral values are : 0,1,2,3,4

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