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(D) Let the circle be $(x - h)^2 + (y - k)^2 = r^2$,where $(h, k)$ is the centre and $r$ is the radius.Since the circle touches the $x$-axis,the radiu

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$A$ hyperbola

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(D) Let the circle be $(x - h)^2 + (y - k)^2 = r^2$,where $(h, k)$ is the centre and $r$ is the radius.Since the circle touches the $x$-axis,the radius $r = |k|$.Thus,the equation of the circle is $(x - h)^2 + (y - k)^2 = k^2$,which simplifies to $x^2 - 2hx + h^2 + y^2 - 2ky = 0$.The circle cuts a chord of length $2l$ from the $y$-axis (where $x = 0$).Substituting $x = 0$ into the equation,we get $y^2 - 2ky + h^2 = 0$.The length of the intercept on the $y$-axis is given by $2\sqrt{k^2 - h^2} = 2l$.Squaring both sides,we get $k^2 - h^2 = l^2$.Replacing $(h, k)$ with $(x, y)$,the locus is $y^2 - x^2 = l^2$,which represents a hyperbola.

$A$ circle touches the $x$-axis and cuts off a chord of length $2l$ from the $y$-axis. The locus of the centre of the circle is

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