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yuradex [85]
3 years ago
12

Write the equation for a parabola with a focus at (-8, -1) and a directrix at y = − 4.

Mathematics
1 answer:
Sidana [21]3 years ago
4 0

Answer:

y = 1/6 x^2 + 8/3 x + 49/6

Step-by-step explanation:

This is a parabola which opens upwards.

The distance of a point (x, y)  from the focus is

√[(x -  -8)^2  + (y - -1)^2] and

the distance of the point from the line y = -4

= y - -4

These distances are equal for a parabola so:

√[(x -  -8)^2  + (y - -1)^2] = y + 4

Squaring both sides:

(x + 8)^2 + (y + 1)^2  = (y + 4)^2

x^2 + 16x + 64 + y^2 + 2y + 1 = y^2 + 8y + 16

x^2 + 16x + 64 + 1 - 16 = 8y - 2y

6y = x^2 + 16x + 49

y = 1/6 x^2 + 8/3 x + 49/6 is the equation of the parabola.

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7 0
3 years ago
A 16- foot board is to be cut into two pieces so that one piece is 4 feet longer the the other. How long will the longer piece b
Dennis_Churaev [7]

Answer:

The longer piece will be 10 feet long.

Step-by-step explanation:

16 - 10 is 6

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therefore the longer piece will be 10 feet long

5 0
3 years ago
J is the midpoint of HK¯¯¯¯¯¯¯ . What are HJ, JK, and HK?
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Since J is the midpoint of HK, that means HK is split into two sections HJ and JK that are the same length.

1) You are told that the m<span>easure of segment HJ = 9x-2 and that of segment JK = 4x+13. Since you also know they are equal lengths, you can set these equations equal to each other to find the value of x!
HJ = JK
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5x = 15
x = 3

2) Now you know x = 3. Plug that into your given equations for HJ and JK to find the length of each segment (or a shortcut would be to find one of them, and then you also know the other is the same length. I'm doing both, just to make sure I don't make a silly mistake!):
HJ = <span>9x-2 
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HJ = 27 - 2
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JK = 4x + 13
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3) Finally, the length of HK is just the length of HJ + JK, or HK = 25 + 25 = 50.

-----

Answer: HJ = 25, JK = 25, HK = 50
4 0
3 years ago
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irinina [24]

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2 years ago
What is 6.213 as a mixed number
Ira Lisetskai [31]
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all you do to convert it to a mixed number is look at how many numbers are after the decimal.

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