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3 years ago

Find the vertex, focus, directrix, and focal width of the parabola.

Mathematics

2 answers:

Slav-nsk [51]3 years ago

7 0

Answer:

Step-by-step explanation:

i just took the edg quiz

ANEK [815]3 years ago

6 0

Answer:

Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16 ⇒ answer (a)

Step-by-step explanation:

* Lets revise some facts about the parabola

- Standard form equation for a parabola of vertex at (0 , 0)

- If the equation is in the form x² = 4py, then

- The axis of symmetry is the y-axis, x = 0

- 4p equal to the coefficient of y in the given equation to

solve for p

- If p > 0, the parabola opens up.

- If p < 0, the parabola opens down.

- Use p to find the coordinates of the focus, (0 , p)

- Use p to find equation of the directri , y= − p

- Use p to find the endpoints of the focal diameter, (±2p , p)

* Now lets solve the problem

- The vertex of the parabola is (0 , 0)

∵ -1/16x² = y ⇒ multiply each side by -16

∴ x² = -16y

∴ 4p = -16 ⇒ ÷ 4 tbe both sides

∴ p = -4

∵ The focus is (0 , p)

∴ The focus is (0 , -4)

∵ The directrix is y = -p

∴ The directrix is y = -(-4) = 4 ⇒ y = 4

∵ The endpoints of the focal diameter, (±2p , p)

∴ The focal width = 2p - (-2p) = 4p

∴ The focal width = 4 × I-4I = 16

* Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16

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Answer:

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Step-by-step explanation:

Given

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Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

$Length = 4 * 13 + 8$

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