Let Q(x_1, y_1) be a variable point and R(1, | vedclass

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(D) Let the coordinates of point $P$ be $(h, k)$.Since $P$ is the mid-point of $QR$,we have:$h = \frac{x_1 + 1}{2}$ and $k = \frac{y_1 + 0}{2}$This im

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

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(D) Let the coordinates of point $P$ be $(h, k)$.Since $P$ is the mid-point of $QR$,we have:$h = \frac{x_1 + 1}{2}$ and $k = \frac{y_1 + 0}{2}$This implies $x_1 = 2h - 1$ and $y_1 = 2k$.Since point $Q(x_1, y_1)$ lies on the circle $x^2 + y^2 = 1$,we substitute the values of $x_1$ and $y_1$ into the circle equation:$(2h - 1)^2 + (2k)^2 = 1$$4h^2 - 4h + 1 + 4k^2 = 1$$4h^2 + 4k^2 - 4h = 0$Dividing by $4$,we get $h^2 + k^2 - h = 0$.Replacing $(h, k)$ with $(x, y)$,the locus of point $P$ is $x^2 + y^2 - x = 0$.

Let $Q(x_1, y_1)$ be a variable point and $R(1, 0)$ be a point on the circle $x^2 + y^2 = 1$. If $P$ is the mid-point of $QR$,then the locus of the point $P$ is:

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