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The locus of the midpoint of the segment joining the focus to a movingpoint on the parabola `y^2=4a x`is another parabola with directrix`y=0`(b) `x=-a``x=0`(d) none of theseA. x = -aB. x = aC. x = 0D. x = a/2 |
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Answer» Correct Answer - C Let `P(at^(2), 2at)` be a moving point on the parabola `y^(2)=4ax` and let S(a, 0) be its focus. Let Q(h, k) be the mid-point of PS. Then, `rArr" "2h=a(k/a)^(2)+a" [On climinating t]"` `rArr" "k^(2)=2a(h-a/2)` Hence, the locus of `"(h, k) is "y^(2)=2a(x-a//2)`. The equation of the directrix of this parabola is `x-a/2=-a/2 rArr x=0` |
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