Find the vertex, focus, directrix, and focal width of the parabola. x = 4y2.

Question

Mathematics

Korbin Vance

28 August, 15:44

Find the vertex, focus, directrix, and focal width of the parabola. x = 4y2.

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Answers (1)

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Barrett Hood · Answer 1

- Vertex : (0, 0).

- Focus: (p/2, 0);

y² = 1/4 x

y² = 2 p x ⇒ 2 p = 1/4

p = 1/8

p/2 = 1/16

F (1/16, 0)

- Directrix:

x = - p/2 x

x = - 1/16 x

- The focal length:

2 p = 2 · 1/8 = 1/4