What is the length of latus rectum of the parabola x^=20y

To find the length of the latus rectum of a parabola, you need to know its equation in standard form. The standard form of a parabola is given by the equation y^2 = 4ax, where "a" is a constant.

In your case, the equation of the parabola is x^2 = 20y. To convert it into standard form, we need to isolate "y" on one side of the equation. Taking the square root of both sides gives you y = (1/20)x^2.

Comparing this to the standard form equation, we see that "a" in this case is 1/20. The latus rectum of a parabola is defined as the line segment parallel to the directrix and passing through the focus. For a parabola given in standard form, the length of the latus rectum is 4a.

Substituting the value of "a" into the formula, we get the length of the latus rectum as:
Length of latus rectum = 4 * (1/20) = 1/5 units.

Therefore, the length of the latus rectum of the parabola x^2 = 20y is 1/5 units.

Recall that for the parabola

x^2 = 4py

the latus rectum has length 4p