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If the normal chord of the parabola `y^(2)=4 x` makes an angle `45^(@)` with the axis of the parabola, then its length, isA. 8B. `8sqrt2`C. 4D. `4sqrt2` |
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Answer» Correct Answer - B The equation of a normal to `y^(2)=4x" at "P(t^(2), 2t)` is `y+tx=2t+t^(3)` This makes an angle of `45^(@)` with x-axis. Therefore, t=-1. If it culs the parabola at `Q(t_(1)_^(2),2t_(1))`, then `t_(1)=-t-2/t=3` Thus, the coordinates of P and Q are (1, -2) and (9, 0) respectively. `:." "PQ=sqrt(64+64)=8sqrt2` |
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