The distance between the focus and the directrix of the parabola is \_\_\_\_\_.
Problem 55
Official solution
To solve, convert the parabola into the standard equation form: .
Therefore, the parabola opens upwards, satisfying .
Since , the focus is at (0, ).
Thus, the coordinates of the parabola's focus are (0, 1).
Furthermore, the equation of the directrix of the parabola is , that is, .
Therefore, the distance between the focus and the directrix of the parabola is .
Hence, the answer is: .
First, convert into the standard equation of an upward-opening parabola, obtaining the coefficient . Then, using the formula, we find the focus coordinates to be (0, 1), and the directrix equation to be . Finally, we can determine the distance from the focus to the directrix of the parabola.
This question uses the parabola of a quadratic function graph as an example, focusing on the basic concepts of the parabola's focus and directrix, and is considered a basic question.