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victus00 [196]
3 years ago
14

What is the equation of a parabola with (−2, 4) as its focus and y = 6 as its directrix? Enter the equation in the box.

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
6 0

Check the picture below.  So the parabola looks more or less like so.

let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.

Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as  you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.

\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-2\\ k=5\\ p=-1 \end{cases}\implies 4(-1)(y-5)=[x-(-2)]^2\implies -4(y-5)=(x+2)^2 \\\\\\ y-5=-\cfrac{1}{4}(x+2)^2\implies y=-\cfrac{1}{4}(x+2)^2+5

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3x+-6+2 > = 5x -8......can someone please solve this
Maksim231197 [3]

Answer:

x ≤ 2

Step-by-step explanation:

If you referencing ">=" as greater than or equal to, follow the solution below:

Solve:

3x - 6 + 2 ≥ 5x - 8

Combine like terms.

3x - 4 ≥ 5x - 8

Subtract 5x from both sides.

-2x - 4 ≥ -8

Add 4 to both sides.

-2x ≥ -4

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Your answer would be x ≤ 2

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3 years ago
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Step-by-step explanation:

Because angles that are vertical to each other are congruent that means 2x+6=96

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