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A point on the curve $x=3 \cos \theta, y=2 \sin \theta$ at which the tangent is perpendicular to $X$-axis is
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$(3,0)$
Given curve is $x=3 \cos \theta, y=2 \sin \theta$ is represent ellipse, $\frac{x^2}{9}+\frac{y^2}{4}=1$ and the tangent perpendicular to $X$-axis can be drawn at end points of the major axis means either at $(3,0)$ or $(-3,0)$.
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