The focal width of a parabola is the distance between its two points on the parabola that are directly above and below the focus. To find the focal width, you first need to know the equation of the parabola.
If the parabola opens upwards or downwards, the standard form of the equation is:
y = ax²
Here, a is a constant that affects the width and the direction of the parabola. The focal width can be calculated using the formula:
Focal Width = |4a|
For example, if you have a parabola described by the equation y = 2x², we identify a = 2. Plugging this value into the focal width formula gives us:
Focal Width = |4 * 2| = 8
This means that for the parabola y = 2x², the focal width is 8 units.
If the parabola opens to the right or left, the equation follows the form:
x = ay²
In this case, the focal width is also found using the same formula: Focal Width = |4a|.