The focal diameter of a parabola, also known as the latus rectum, is a line segment that passes through the focus of the parabola and is perpendicular to the axis of symmetry. To find the focal diameter, you can use the following steps:
- Identify the equation of the parabola: The standard form of a parabola that opens upward is given by the equation y = ax². For a parabola that opens sideways, the equation takes the form x = ay².
- Determine the value of ‘a’: In the standard equations, the coefficient ‘a’ indicates the direction and width of the parabola. If your equation is in vertex form, y = a(x – h)² + k or x = a(y – k)² + h, simply extract the ‘a’ value.
- Calculate the focal diameter: The focal diameter is given by the formula Focal Diameter = |4p|, where ‘p’ is the distance from the vertex to the focus. For the parabola y = ax², ‘p’ can be calculated as p = 1/(4a). Hence, the focal diameter will be |4(1/(4a))| = |1/a|.
For example, if you have a parabola represented by the equation y = 2x², then ‘a’ is 2. The focal diameter would be |1/2| = 0.5.
This means the distance of the latus rectum (focal diameter) is 0.5 units. In summary, just find the ‘a’ value from your parabola’s equation and apply it to the formula to find the focal diameter.