1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
Seamstress Jane has purchased 50 yards of red fabric and 110 yards of gold fabric to make red and gold curtains. What is the lar
Alisiya [41]

Answer: There are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.

There are 5 red fabrics and 11 gold fabrics that would be used for each curtain.

Step-by-step explanation:

Since we have given that

Number of yards of red fabric purchased by Jane = 50

Number of yards of gold fabric purchased by Jane = 110

We need to find the largest number of curtains she can make if she wants all the curtains to be exactly the same length.

For this we will find H.C.F. of 50 and 110.

Factors of 50 = 1, 2, 5, 10, 25, 50.

Factors of 110 = 1, 2, 5, 10, 11, 22, 55, 110.

So, Highest common factor of 50 and 110 is 10.

So, there are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.

Number of yards of red fabric is given by

\frac{50}{10}=5

Number of yards of gold fabric is given by

\frac{110}{10}=11

Hence, there are 5 red fabrics and 11 gold fabrics that would be used for each curtain.

4 0
3 years ago
What multiplied by 3 equals 15 but added by 3 equals 18
Ivenika [448]

Answer:

15

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65 minutes. Suppose the actual commu
n200080 [17]

Answer:

I would say about 10% chance.

5 0
3 years ago
A kite has side lengths of 2 feet and 4 feet. Each side length is increased by the same number of feet. The expression represent
inysia [295]
The x terms add up to 4x and the numbers add up to 12
 4x + 12 = 4(x + 3)


Its C
4 0
2 years ago
Read 2 more answers
How can I find the slope and Y- intercept for each equation
mixer [17]
Answer:

You plug in numbers into the y=mx+b equation and solve for which ever one you are finding for.
m=slope
x=x intercept
b=y intercept
apply the numbers to this equation and solve or x
7 0
3 years ago
Other questions:
  • Hey guys! This is super hard. So if you don't mind, can you help me? :)
    5·2 answers
  • The perimeter of a rectangle is 20 cm. The length is 7 cm. What is the area?
    14·1 answer
  • I'm just confused on all of it
    5·1 answer
  • 7 &lt; 12 + c &lt; 13<br><br><br> Pls help me show work
    14·2 answers
  • A chair for an adult is 20 in. tall and 16 in. wide. A builder
    9·1 answer
  • The side lengths of a square are each 3p. By adding 5 to the length and subtracting 5 from the width, a rectangle is made. What
    7·1 answer
  • you have a coupon for 25% off at the record store, and the cd you want retails for $19.96. how much will it cost you?
    12·2 answers
  • Combine like terms:
    12·1 answer
  • What is the percentage of sugar in the syrup made of 10 kg of water and 5 kg of sugar?
    7·1 answer
  • Simplify.<br> 1/2(4x-10)
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!