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Find the coordinates of the focus and th...

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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