The parabola having its focus at $(3, 2)$ and directrix along y-axis has its vertex at:

(\frac{3}{2}, 1)

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(\frac{3}{2}, 2)

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(\frac{3}{2}, \frac{1}{2})

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(\frac{3}{2}, - \frac{1}{2})

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Solution

The correct option is B $(\frac{3}{2}, 2)$
Equation of directrix is $x = 0$ .
We know axis of parabola is perpendicular to its directrix and passes through the focus.
Hence, it's equation is $y = 2$
Now vertex of the parabola will be mid-point of foot of directrix and the focus.
i.e mid point of $(3, 2)$ and $(0, 2)$ which is $(\frac{3}{2}, 2)$

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The parabola having its focus at (3,2) and directrix along y-axis has its vertex at:

The parabola having its focus at $(3, 2)$ and directrix along y-axis has its vertex at: