Answer:
The equation of the parabola is:
[tex]y=\dfrac{1}{10}x^2[/tex]
Step-by-step explanation:
Since the directrix is the line y = -2.5, this is a horizontal line ; thus the parabola opens up or down.
[tex](x - h)^2 = 4p (y - k)[/tex] , where (h, k) is the vertex, the focus is (h, k + p), and the directrix is y = k - p.
The vertex is (h, k), or (0,0)
The directrix is y = -2.5
so k - p = -2.5
⇒ 0 - p = -2.5
⇒ p = 2.5
The focus is (h, k + p)
⇒ (0, 0 +2.5)=(0, 2.5)
Thus substituting the values into the base equation,
[tex](x - h)^2 =4p(y-k)\\\\(x - 0)^2 = 4\times (2.5)\times (y-0)\\\\x^2 =10y\\\\y=\dfrac{1}{10}x^2[/tex]
Hence the equation of the parabola is:
[tex]y=\dfrac{1}{10}x^2[/tex]
