Question

What are the focus and directrix of the parabola with the equation y=1/12x^2

Answer 1

The focus of the parabola is (0, 3) and the directrix is the line y = -3.

Step-by-step explanation:

The equation y = 1/12x^2 represents a parabola. To find the focus and directrix of the parabola, we can use the vertex form of the equation: y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

In this case, a = 1/12. The vertex is located at (h, k) = (0, 0). The focus is a point inside the parabola, and it is located at a distance equal to 1/4a units above the vertex. Therefore, the focus of the parabola is (0, 1/(4a)) = (0, 3).

The directrix of the parabola is a horizontal line that is a distance equal to 1/4a units below the vertex. Therefore, the directrix of the parabola is the line y = -1/(4a) = -3.

Answer 2

The focus of the parabola with equation y = 1/12x^2 is at (0, 1/6), and the directrix is the line y = -1/6.

Step-by-step explanation:

The equation y = \frac{1}{12}x^2 represents a parabola that opens upwards. The coefficient of the x^2 term, which is a, gives us information about the focus and directrix of the parabola. For a parabola with the equation y = ax^2, the focus is at (0, 1/(4a)) and the directrix is the line y = -1/(4a). Thus, for the given parabola, the focus is at (0, 1/6) and the directrix is y = -1/6.