What is the length of the latus rectum of x^2=20y
X squared equals twenty Y
To find the length of the latus rectum of the equation x^2 = 20y, we need to understand the basic concept of a parabola and its latus rectum.
A parabola is a U-shaped curve that can be defined by a quadratic equation of the form y = ax^2 + bx + c. In this case, the equation given is x^2 = 20y, which is a simplified form where a = 1, b = 0, and c = 0.
The latus rectum of a parabola is a line segment that is perpendicular to the axis of the parabola and passes through the focus. The length of the latus rectum for a parabola with the equation y^2 = 4ax is equal to 4a.
From the given equation x^2 = 20y, we can rewrite it in the form y = (1/20)x^2. Comparing it with the general equation y^2 = 4ax, we can see that a = 1/20.
Now, we can find the length of the latus rectum by substituting the value of a into the formula: latus rectum = 4a.
latus rectum = 4 * (1/20) = 4/20 = 0.2 (or 1/5)
Therefore, the length of the latus rectum for the equation x^2 = 20y is 0.2 (or 1/5) units.