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2 years ago

A parabola can be drawn given a focus of (0,−6) and a directrix of y=−2. Write the equation of the parabola in any form.

Mathematics

1 answer:

topjm [15]2 years ago

7 0

Answer:

y = x^2 - 4

Step-by-step explanation:

The vertex of a parabola is exactly halfway between the focus and the directrix. If the focus is at (0, -6) and the directrix is the line y = -2, then we do this to locate the vertex: Draw a vertical line through (0, -6) also crossing the line y = -2. The y value halfway between y = -6 and y = -2 is y = -4, and the vertex is thus (0, -4).

Using the vertex method, write out the equation of this parabola, starting with the general form y - k = (x-h)^2, where (h, k) is the vertex. Here h = 0 and k = -4

We get: y + 4 = (x - 0)^2, or y + 4 = x^2, or y = x^2 - 4. As a check, let x = 0; y = -4, which is the y-coordinate of the vertex.

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ArbitrLikvidat [17]

Answer:

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Step-by-step explanation:

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kupik [55]

Answer:

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Step-by-step explanation:

Given

Options (a) to (d)

Required

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From the given options (a) to (d), only $x \le 5$ fits the above description.

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To further explain this;

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2 years ago

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Volgvan

Answer:

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Read 2 more answers

The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (includin

babunello [35]

Answer:

He should plant 100 acres of corn and 400 acres of wheat.

Step-by-step explanation:

This problem can be solved by a siple system of equations.

]x denotes the number of acres of corn

y denotes the number of acres of wheat

Building the system:

The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. This means that:

$x + y = 500$

The cost of cultivating corn and wheat (including seeds and labor) is $42 and $30 per acre, respectively. Jacob Johnson has $16,200 available for cultivating these crops. This means that:

$42x + 30y = 16,200$