To find the equation of the directrix of the parabola x^2-30y=0, we need to express the equation in the standard form of a parabola by completing the square.
x^2 - 30y = 0
x^2 = 30y
We can see that the parabola opens upward, which means the directrix will be a horizontal line.
Since the directrix is a horizontal line and the vertex of the parabola is at the origin (0,0), the equation of the directrix can be written as y = -p, where p is the distance from the origin to the directrix.
In order to find p, we will use the standard form of a parabola where p is the distance from the vertex to the focus of the parabola.
The general form for a parabola is (x - h)^2 = 4p(y - k), where (h, k) is the vertex.
Comparing this form with the equation x^2 = 30y, we can see that h = 0 and k = 0.
So, the vertex is (0, 0) and p is the distance from the vertex to the focus, which is the same as the distance from the vertex to the directrix.
Using the distance formula, we can find the distance from the vertex to the directrix:
p = sqrt(30)
Therefore, the equation of the directrix is:
y = -sqrt(30)
What is the equation of the directrix of the parabola whose equation is x2-30y=0 ?
1 answer