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Yakvenalex [24]
2 years ago
12

Write the equation for a parabola with a focus at (1,2)(1,2)left parenthesis, 1, comma, 2, right parenthesis and a directrix at

y=6y=6y, equals, 6.
y=
Mathematics
1 answer:
Tanya [424]2 years ago
6 0

Answer:

  y = -1/8(x -1)² +4

Step-by-step explanation:

The equation of a parabola can be written from focus and directrix using the form ...

  y = 1/(4p)(x -h)² +k

where p is the distance from vertex to focus, and (h, k) is the vertex.

The vertex-focus distance is half the distance from the directrix to the focus. Here, that is ...

  p = (2 -6)/2 = -4/2 = -2

The vertex is halfway between the focus and directrix on the same vertical line, so has coordinates ...

  (h, k) = ((1, 2) +(1, 6))/2 = (1, 4)

__

Using these values of p and (h, k), we find the equation of the parabola to be ...

  y = 1/(4(-2))(x -1)² +4

  y = -1/8(x -1)² +4

_____

<em>Additional comment</em>

You can check the graph by considering the definition of a parabola: each point on the curve is equidistant from the focus and the directrix. This is easily verified for points on the horizontal and vertical lines through the focus. For example, point (5, 2) is 4 units from the focus, and 4 units from the directrix.

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Two factory plants are making tv panels. Plant A produced 2000 fewer panels than Plan B did. Two percent of the panels from Plan
Serggg [28]

Answer:

Plant A produced 15,000 panels.

Step-by-step explanation:

Let plant B produce x panels

Plant A then produced x - 2000 panels

2% of panels from plant A were defective

3% of panels from plant B were defective

The two plants together produced 810 defective panels so;

2/100(x - 2000) + 3/100(x) = 810

0.02x - 40 + 0.03x = 810

0.05x = 850

x = 17,000 panels

So plant B produced 17,000 panels

Plant A produced 17,000 - 2,000 panels = 15,000 panels.

8 0
3 years ago
-7 2/3 +(5 1/2) + 8 3/4 =
drek231 [11]

Answer:

6  7/12

Step-by-step explanation:

-7 2/3 +(5 1/2) + 8 3/4

Get a common denominator of 12

-7 2/3 * 4/4 +(5 1/2 +6/6) + 8 3/4*3/3

-7 8/12    + 5 6/12     + 8 9/12

Subtract the  first two terms first

They have opposite signs so subtract and take the sign of the larger

-7 8/12    + 5 6/12    = -2 2/12

-2  2/12 + 8 9/12

They have opposite signs so subtract and take the sign of the larger

-2  2/12 + 8 9/12 = 6 7/12

7 0
3 years ago
I NEED HELP WITH THIS PROBLEM
allochka39001 [22]
In a triangle, the midline joining the midpoints of two sides is parallel to the third side and half as long

2(5x+2) = 3x + 32
10x + 4 = 3x + 32
10x - 3x = 32 - 4
7x = 28
x = 28/7
x = 4

The length of the midsegment = 5x+2 = 5·4 + 2 = 22
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3 years ago
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Angelina_Jolie [31]

Answer:

B

Step-by-step explanation:

If you notice, since concert tickets is 1, the cost is $23. So we are finding an option that satifies that. The only option is B.

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5 0
2 years ago
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Dilate the point B(-4,5) by a scale factor of 3 with the center at the origin.
malfutka [58]
Answer: B (-12, 15)

Step: (3×-4) =-12
And (3×5)= 15
5 0
3 years ago
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