Let P be the point (1, 0) and Q be a point on | vedclass

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(A) Let the coordinates of point $Q$ on the parabola $y^2 = 8x$ be $(2t^2, 4t)$.Let the midpoint of $PQ$ be $(h, k)$.Since $P = (1, 0)$ and $Q = (2t^2

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$y^2 - 4x + 2 = 0$

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(A) Let the coordinates of point $Q$ on the parabola $y^2 = 8x$ be $(2t^2, 4t)$.Let the midpoint of $PQ$ be $(h, k)$.Since $P = (1, 0)$ and $Q = (2t^2, 4t)$,the midpoint $(h, k)$ is given by:$h = \frac{2t^2 + 1}{2} \implies 2t^2 = 2h - 1$$k = \frac{4t + 0}{2} = 2t \implies t = \frac{k}{2}$Substitute $t = \frac{k}{2}$ into the equation $2t^2 = 2h - 1$:$2(\frac{k}{2})^2 = 2h - 1$$2(\frac{k^2}{4}) = 2h - 1$$\frac{k^2}{2} = 2h - 1$$k^2 = 4h - 2$Replacing $(h, k)$ with $(x, y)$,the locus is $y^2 = 4x - 2$,which is $y^2 - 4x + 2 = 0$.

Let $P$ be the point $(1, 0)$ and $Q$ be a point on the parabola $y^2 = 8x$. Find the locus of the midpoint of $PQ$.

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