Explanation:
1.What is the equation of a parabola with a vertex at (0, 0)?
y = ax²; y = -ax²; x = ay²; x = -ay² where a = [½, 1 , 2]
Also an infinity of others at various values of a and various angles.
2.The focus lies above the vertex, so the parabola is vertical and the focal length p=10.25
Equation for up-opening parabola with vertex (h,k) and focal length p:
y=14p(x−h)2+k
y=14p(x−0)2+0y=141x2
3.Since the directrix is the line y=−10.25 , a point (x,y) is on the parabola if, and only if,
x2+(y−10.25)2=(y+10.25)2.
Therefore, x2−20.5y=20.5y and y=141x2.
hope I helped