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(C) Let the focus of the parabola be $F = (3, 2)$.The tangents at the endpoints of the latus rectum of a parabola intersect at the point where the axi

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$x - y = 1$

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(C) Let the focus of the parabola be $F = (3, 2)$.The tangents at the endpoints of the latus rectum of a parabola intersect at the point where the axis of the parabola meets the directrix.This intersection point lies on the line $x + y = 2$.Since the axis of the parabola passes through the focus $(3, 2)$ and is perpendicular to the directrix,and the intersection point of the tangents lies on the axis,the axis must pass through the point of intersection of the tangents.However,the problem states the tangents intersect on the line $x + y = 2$. The intersection point of the tangents at the ends of the latus rectum is the point where the axis meets the directrix.Let the intersection point be $P(h, k)$. Since $P$ lies on $x + y = 2$,we have $h + k = 2$.The axis passes through the focus $(3, 2)$ and the point $P(h, k)$.The slope of the axis is $m = \frac{2 - k}{3 - h}$.Since the directrix is perpendicular to the axis,and the intersection point $P$ lies on the directrix,the line $x + y = 2$ is not necessarily the directrix,but the intersection point lies on it.Given the standard properties,the axis of the parabola is the line passing through the focus $(3, 2)$ and perpendicular to the directrix.By testing the options,the line $x - y = 1$ passes through $(3, 2)$ since $3 - 2 = 1$. Thus,$x - y = 1$ is the correct axis.

The tangents drawn at the endpoints of the latus rectum of a parabola $S = 0$ intersect on the line $x + y = 2$. If $(3, 2)$ is the focus of the parabola,then the axis of the parabola $S = 0$ is:

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