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Kushal Sirish Dada
Asked: 2022-10-30T19:13:32+05:30 In:

The complete set of values of the parameter `alpha` so that the point `P(alpha, (1 +alpha^(2))^(-1))` does not lie outside the triangle formed by the lines `L_(1): 15y = x +1, L_(2) : 78y = 118 – 23x` and `L_(3):y +2 = 0` is
A. `(0,5)`
B. `[2,5]`
C. `[1,5]`
D. `[0,2]`

The complete set of values of the parameter `alpha` so that the point `P(alpha, (1 +alpha^(2))^(-1))` does not lie outside the triangle formed by the lines `L_(1): 15y = x +1, L_(2) : 78y = 118 – 23x` and `L_(3):y +2 = 0` is
A. `(0,5)`
B. `[2,5]`
C. `[1,5]`
D. `[0,2]`
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  1. Correct Answer – C
    As `P(alpha,(1+alpha^(2))^(1-))` lie on `y = (1)/(1+x^(2))` which never intersect the line `y =-2`
    `:.` On solving `y = (1)/(1+x^(2))` with `L_(1)`, we get `P_(1) (2,(1)/(5))` (i)
    and the `L_(2)`, we get `P_(2)(5,(1)/(26))` (ii)
    `:.` From (i) and (ii), we get `2 le alpha le 5`

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