If P is (3, 1) and Q is a point on the curve | vedclass

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(B) Let $P = (3, 1)$ and $Q = (x_1, y_1)$ be a point on the parabola $y^2 = 8x$. Let $R(h, k)$ be the mid-point of the line segment $PQ$. By the mid-p

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$4y^2 - 16x - 4y + 25 = 0$

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(B) Let $P = (3, 1)$ and $Q = (x_1, y_1)$ be a point on the parabola $y^2 = 8x$. Let $R(h, k)$ be the mid-point of the line segment $PQ$. By the mid-point formula,we have: $h = \frac{3 + x_1}{2} \implies x_1 = 2h - 3$ $k = \frac{1 + y_1}{2} \implies y_1 = 2k - 1$ Since $Q(x_1, y_1)$ lies on the parabola $y^2 = 8x$,we substitute the coordinates of $Q$: $(2k - 1)^2 = 8(2h - 3)$ $4k^2 - 4k + 1 = 16h - 24$ $4k^2 - 4k - 16h + 25 = 0$ Replacing $(h, k)$ with $(x, y)$,the locus is: $4y^2 - 4y - 16x + 25 = 0$

If $P$ is $(3, 1)$ and $Q$ is a point on the curve $y^2 = 8x$,then the locus of the mid-point of the line segment $PQ$ is

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