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Find the coordinates of the focus and the vertex, the equations of the directix and the axis, and the lendth of the latus rectum of the parabola `x^(2)=6y`

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The given equations is of the form `x^(2)=-4ay"where "4a=6,i.e. a=(3)/(2)`.So, this is a case of upward parabola. Its focus is `F(0,a),i.e. F(0,(3)/(2))` Its vertex is O(0,0). The equation of the directrix is y=-a i.e, `y=(3)/(2)`. Its axis is y-axis, whose equations is x=0. Length of latcus rectum=`4a=(4xx(3)/(2))`units=6units.
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