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
\(x^2=20y\)
we have to find the vertex, focus, directrix, and focal width of the parabola.
Parabola: \(x^2=20y\)
\(\text{standard equation of parabola}x^2=4by\)
Comparing, we get
\(4b=20\) ⇒ \(b=\frac{20}{4}=5\)
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.
