Let `A (0,2),B` and C be points on parabola `y^(2)+x +4` such that `/_CBA (pi)/(2)`. Then the range of ordinate of C is (a) `(-oo,0)uu (4,oo)` (b) `(-oo,0] uu[4,oo)` (c) `[0,4]` (d) `(-oo,0)uu [4,oo)`

Options

A. `(-oo,0)uu (4,oo)`
B. `(-oo,0] uu[4,oo)`
C. `[0,4]`
D. `(-oo,0)uu [4,oo)`

Answer

B

Explanation

`A(0,2), B= (t_(1)^(2)-4,t_(1)), C =(t^(2) -4,t)`
`/_CBA = (pi)/(2)`
`rArr (2-t_(1))/(4-t_(1)^(2)). (t_(1)-t)/(t_(1)^(2)-t^(2)) =-1`
`rArr (1)/(2+t_(1)). (1)/(t+t_(1)) =-1`
`rArr t_(1)^(2) + (2+t) t_(1) + (2t+1) =0`
For real `t_(1), (2+t)^(2) -4(2t-1) = t^(2) - 4t ge 0`
`rArr t in (-oo,0] uu[4,oo)`