What is the focus of the parabola that has a vertex at (0, 0) and that passes through the points (–3, 3) and (3, 3)?

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Answer 1 · 2016-06-27T05:31:38

Focus is #S(0, 3/4)#. The equation of the parabola is #x^2=3y#. The size #a = 3/4#..

As #(+-3, 3) are equidistant from the y-axis, y-axis is the axis

of the parabola. O(0, 0) is the vertex. Therefore, its equation is

of the form

#x^2=4ay#.

This passes through #(+-3, 3)#. 9 = 12a. So,

#a = 3/4#..

The focus is on the axis x = 0, at a distance a = 3/4, from

the vertex (0, 0).

Thus the focus is #S(0, 3/4)#.