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
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.

You might be interested in
6 less than one-third of a number m is y
nekit [7.7K]

<u><em>Answer:</em></u>

(m×1/3)-6=y

<u><em>Step-by-step explanation:</em></u>

  1. Start with m as the unknown variable.
  2. Now multiple that by 1/3 to find that portion of m. (m×1/3)
  3. Lastly, subtract 6 and set the expression equal to y. (-6=y)
  4. Thus we get our final equation: (m×1/3)-6=y
7 0
2 years ago
14. This week, Anita spent 3 1/2 h practicing the piano. She also spent 6 1/4 h at soccer practice and 4 1/3 h on the telephone.
gizmo_the_mogwai [7]

Answer:  a)9 3/4 hours

B)1 11/12 hour

Step-by-step explanation:

Piano: 3 1/2 hour; 3hours 30min

Soccer: 6 1/4 hour; 6hours and 15 min

Telephone: 4 1/3 hour; 4 hours and 20 min.

Remember that in an hour there is 60 min, and 1/2 of an hour is 30 (min), 1/4  is 15(min) and 1/3 is 20(min).

a) 3hours and 30min + 6hours and 15 min

That gives us 9 hours and 45 min, which is 9 3/4 hours.

B) 6hours and 15 min — 4 hours and 20 min

That gives us 1 hour and 55 min, which is 1 11/12 hours.

I hope this helps you!

7 0
2 years ago
A sales person works 40 hours per week at a job he has two options were being paid option is the hourly wage of $19 I should be
gladu [14]
It should be 6& all you wanna do you youuuu
5 0
2 years ago
Suppose that a certain movie earns $3,000,000 in ticket sales. If 60% goes to the movie and 40% goes to theatres: Movie studios
miskamm [114]

Answer: See explanation

Step-by-step explanation:

Amount earned by movie = $3,000,000.

Percentage that went to movie = 60%

Percentage that went to theater = 40%

Revenue gotten by movie studio = 60% × $3,000,000

= 0.6 × $3,000,000

= $1,800,000

Revenue gotten by theaters = 40% × $3,000,000

= 0.4 × $3,000,000

= $1,200,000

5 0
3 years ago
HELP ASAP PLZ IM TIMED
nasty-shy [4]

Answer:

70

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • Find the slope between points (4, 6) and (-2, 6).
    14·1 answer
  • explain how the graph of y=-2sin(x)-1 differs from the parent function. Make sure to compare key points used for graphing
    11·1 answer
  • Where are earthquakes and volcanoes most likely to occur ?
    15·2 answers
  • A customer at the mall is shopping for holiday gifts, and is considering having them wrapped. He can get them wrapped at the dep
    8·1 answer
  • Help!!!!!!!!!!!!!!!!!!!!
    7·1 answer
  • 3kg of salt is add to 15kg of pure water. What percentage of the mixture is salt?
    10·1 answer
  • What is the solution to 5x + 3(x - 5) = 6x + 2x - 15
    9·2 answers
  • A set of biology exam scores are normally distributed with a mean of 70 points and a standard deviation of 6
    9·2 answers
  • There are 2 green pens, 3 blue pens, 4 red pens, and 1 black pen in the teachers desk. The teacher selects 2 pens at random, and
    14·1 answer
  • The city of Raleigh has 11000 registered voters. There are two candidates for city council in an upcoming election: Brown and Fe
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!