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If the parabols `y^(2) = 4kx (k gt 0)` and `y^(2) = 4 (x-1)` do not have a common normal other than the axis of parabola, then `k in`A. `(0,1)`B. `(2,oo)`C. `(3,oo)`D. `(0,oo)` |
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Answer» Correct Answer - A::B::C If the parabolas have a common normal of slope `m(m ne 0)` then it is given by `y = mx - 2km -km^(3)` and `y = m(x-1) -2m -m^(3) = mx -3m -m^(3)` `rArr 2km + km^(3) = 3m + m^(3)` `rArr m = 0, m^(2) =(3-2k)/(k-1)`. If `m^(2) lt 0` then the only common normal is the axis. `rArr (3-2k)/(k-1) lt 0` `rArr (k-1) (2k-3) gt 0` `k gt (3)/(2)` or `k lt 1` and `k gt 0` |
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