# 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)?

Jun 27, 2016

Focus is $S \left(0 , \frac{3}{4}\right)$. The equation of the parabola is ${x}^{2} = 3 y$. The size $a = \frac{3}{4}$..

#### Explanation:

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

${x}^{2} = 4 a y$.

This passes through $\left(\pm 3 , 3\right)$. 9 = 12a. So,

$a = \frac{3}{4}$..

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

the vertex (0, 0).

Thus the focus is $S \left(0 , \frac{3}{4}\right)$.