Answer:
Directrix is line with equation y=-5 and focus is the point with coordinates (0,5) with vertex (0,0) and focal width 20 units.
Step-by-step explanation:
Given the equation of parabola i.e
[tex]x^2=20y[/tex]
we have to find the vertex, focus, directrix, and focal width of the parabola.
Parabola: [tex]x^2=20y[/tex]
[tex]\text{standard equation of parabola}x^2=4by[/tex]
Comparing, we get
[tex]4b=20[/tex] ⇒ [tex]b=\frac{20}{4}=5[/tex]
Vertex: (0,0)
Focus: (0,b)=(0,5)
Directrix: y=-b ⇒ y=-5
Focal width: 4(5) = 20 units
Directrix is line with equation y=-5 and focus is the point with coordinates (0,5) with vertex (0,0) and focal width 20 units.
