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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 isA. `(-oo,0)uu (4,oo)`B. `(-oo,0] uu[4,oo)`C. `[0,4]`D. `(-oo,0)uu [4,oo)` |
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Answer» Correct Answer - B `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)` |
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