Find the vertex, focus, directrix, and focal width of the parabola. x2 = 20y

Mathematics

2 answers:

Lana71 [14]2 years ago

5 0

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.

sp2606 [1]2 years ago

4 0

The parabola :
x² = 20 y
It is in the standard form : x² = 4 b y
b = 20 : 4 = 5
Vertex : ( 0, 0 );
Focus : ( 0, 5 );
Directrix : y + 5 = 0; y = - 5
Focal width: 4 * 5 = 20 units
Answer: A )

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