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 $S(0, 3/4)$ .