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`P` and `Q` are two distinct points on the parabola, `y^2 = 4x` with parameters `t` and `t_1` respectively. If the normal at `P` passes through `Q`, then the minimum value of `t_1 ^2` isA. 4B. 6C. 8D. 2 |
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Answer» Correct Answer - C The coordinates of P and Q are `(t^(2), 2t)` and `(t_(1)^(2), 2t_(1))` respectively. The normal at P passes through Q. `:." "t_(1)=-t-2/trArrt_(1)^(2)rArrt_(1)^(2)+4/t^(2)+4` `"Now, "AM geGM` `rArr" "t^(2)+4/t^(2)ge2sqrt(t^(2)xx4/t^(2))rArrt^(2)+4/t^(2)ge4rArrt_(1)^(2)ge8` Hence, the minimum value of `t_(1)^(2)` is 8. |
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