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miss Akunina [59]
3 years ago
12

Write an equation for a parabola with a focus of (1,-2) and a directrix of y=6

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
8 0

Answer:

y = - \frac{1}{16}(x - 1)² + 2

Step-by-step explanation:

Any point (x, y) on the parabola is equidistant from the focus and the directrix.

Using the distance formula

\sqrt{(x-1)^2+(y+2)^2^} = | y - 6 |

Square both sides

(x - 1)² + (y + 2)² = (y - 6)² ( expand the factors in y )

(x - 1)² + y² + 4y + 4 = y² - 12y + 36 ( subtract y² - 12y from both sides )

(x - 1)² + 16y + 4 = 36 ( subtract 4 from both sides )

(x - 1)² + 16y = 32 ← subtract (x - 1)² from both sides )

16y = - (x - 1)² + 32 ( divide all terms by 16 )

y = - \frac{1}{16} (x - 1)² + 2

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Does anyone know what -23= 13w+2w+22 is plz help!
AlladinOne [14]

Answer:

w = -3

Step-by-step explanation:

-23 = 13w + 2w + 22

Combine like terms (add 13w and 2w and subtract 22 from both sides)

-45 = 15w

Divide both sides by 15

w = -3

4 0
3 years ago
Can anyone tell me the standard form of this parabola equation?
irina [24]

Answer:

x=4y^2-24y+30

(x-4.5)^2+(y-2.5)^2=23

Step-by-step explanation:

Standard form of a sideways parabola:  x=ay^2+by+c

Given equation:

4y^2-x-24y+30=0

Add x to both sides:

4y^2-24y+30=x

\implies x=4y^2-24y+30

--------------------------------------------------------------------------------------------

<u>Standard form of circle equation</u>

(x-a)^2+(y-b)^2=r^2

(where (a,b) is the center and r is the radius)

Given equation:

2x^2+2y^2-18x-10y+7=0

Group like terms:

2x^2-18x+2y^2-10y+7=0

Divide by 2:

x^2-9x+y^2-5y+3.5=0

Factor by completing the square for each variable:

(x-4.5)^2-20.25+(y-2.5)^2-6.25+3.5=0

Rearrange into standard form:

(x-4.5)^2+(y-2.5)^2=23

Therefore, the circle has a center at (4.5, 2.5) and a radius of √23

7 0
2 years ago
Mathew ran 3/8 mile and then walked 7/10 mile which pair of fractions can he use to find how far he went in all
jeka57 [31]

Answer:

15/40 and 28/40

Step-by-step explanation:

3/8 = 15/40

7/10 = 28/40

15+28=43

1 3/40

(I wasn't sure what the question really wanted)

xx

5 0
3 years ago
What are the coefficients of 4x -7 - 8x +17
Vladimir79 [104]
The coefficients are the numbers next to a variable (which is X in this case). Therefore, the coefficients here are 4 and 8
8 0
3 years ago
Perform the indicated row operations:<br> -10r2 r2 3r3 <br> [2 -1 -4|7] [0 3 -2|5] [0 10 8|2]
n200080 [17]

Answer:

Second one is -30, 20, -50

Third one is 30, 24, 6

Step-by-step explanation:

6 0
3 years ago
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