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
frez [133]
2 years ago
12

Write the equation of a parabola with focus at (1,-4) and a directrix at X=2

Mathematics
1 answer:
konstantin123 [22]2 years ago
3 0

Answer:

The equation of a parabola is

x =  \frac{1}{4(f - h)} (y - k) ^{2}  + h

Step-by-step explanation:

(h,k) is the vertex and (f,k) is the focus.

Thus, f = 1, k = −4.

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f - h = h - 2.

Solving the system, we get h = 3/2, k = -4, f = 1.

The standard form is:

x =  -  \frac{y ^{2} }{2}  - 4y -  \frac{13}{2}

The general form is:

2x +  {y}^{2}  + 8y + 13 = 0

The vertex form is:

x =  -  \frac{(y + 4) ^{2} }{2}  +  \frac{3}{2}

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = -4.

The focal length is the distance between the focus and the vertex: 1/2.

The focal parameter is the distance between the focus and the directrix: 1.

The latus rectum is parallel to the directrix and passes through the focus: x = 1.

The length of the latus rectum is four times the distance between the vertex and the focus: 2.

The eccentricity of a parabola is always 1.

The x-intercepts can be found by setting y = 0 in the equation and solving for x.

x-intercept:

( -  \frac{13}{2}  \: ,0)

The y-intercepts can be found by setting x = 0 in the equation and solving for y.

y-intercepts:

(0, - 4 -  \sqrt{3)}

(0, - 4 +  \sqrt{3)}

You might be interested in
Do you guys ever just sit there and realize how not ok you are?
ludmilkaskok [199]
Are you ok? do you want to talk about it babe?
6 0
2 years ago
Read 2 more answers
2p2 - 5p + 3<br> pliss anwered this for me​
Iteru [2.4K]

Answer:

2p²-5p+3 is the final answer as they aren't any like terms to collect in order to simply the solution further.

Step-by-step explanation:

Wishing you a splendiferous day,

stay salty...

7 0
2 years ago
Please tel me what goes where
maria [59]

Step-by-step explanation:

A- Equilateral (all of the angles are the same)

B- isosceles (just two angles are the same)

C- scalene (non of the angles are the same)

7 0
2 years ago
Read 2 more answers
Need help thank you mark brainliest
aliina [53]

Answer: it says independent work

Step-by-step explanation:

3 0
3 years ago
If there were 310 million people in the United States, what was the daily consumption rate in barrels per person in the United S
bija089 [108]

The daily consumption rate in the United States will be 10 barrels per person.

Your question is incomplete as you didn't provide the total barrels, therefore, an overview of the answer will be given. In their case, let's assume that the total barrels is given as 3.1 billion.

Therefore, the barrels per person will be:

= Total barrels / Population

= 3.1 billion / 310 million

= 10 barrels per person.

In conclusion, the correct option is 10 barrels per person.

Read related link on:

brainly.com/question/25261899

7 0
2 years ago
Other questions:
  • Erin has $52 to spend at the florist. She wants to buy a vase for $11.75 and several roses for $3.50 each. What are the possible
    5·1 answer
  • A baker uses 2.327 kilograms of blueberries for muffins. There are four packages at the fruit market. Which amount is closest to
    6·1 answer
  • Using the technique in the model above, find the missing side in this 30°-60°-90° right triangle.
    8·2 answers
  • What is √34cos(x-46.7) =4
    14·1 answer
  • On the coordinate plane below, Point P is located at (2,-3), and point Q is located at (-4,4).
    14·1 answer
  • What is the best estimate of the correlation coefficient for the variables in the scatter plot
    12·2 answers
  • Please help lot of points at stake- and will give brainly.
    7·1 answer
  • What is the geometric mean of 3 and 18
    5·2 answers
  • Graph x-5y=20 <br> please show me the steps
    5·1 answer
  • A.118<br> B.242<br> C.180<br> D.149
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!