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let `P` be the point `(1, 0)` and `Q` be a point on the locus `y^2= 8x`. The locus of the midpoint of `PQ` isA. `x^(2)-4y=2=0`B. `x^(2)+4y+2-0`C. `y^(2)+4x+2=0`D. `y^(2)-4x+2=0` |
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Answer» Correct Answer - D Let R(h, k) be the mid-point of PQ and the coordintes at Q be `(alpha, beta)`. Then, `(alpha+1)/2=h" and "(beta+0)/2=krArralpha=h-1" and "beta=2k` Since `Q (alpha, beta)` lies on the parabola `y^(2)=8x.` `:." "beta^(2) -8alpharArr4k^(2)=8(2h-1)rArrk^(2)=4k-2` Hence, the locus of (h, k) is `y^(2)=4x-2` |
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