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
victus00 [196]
3 years ago
14

What is the equation of a parabola with (−2, 4) as its focus and y = 6 as its directrix? Enter the equation in the box.

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
6 0

Check the picture below.  So the parabola looks more or less like so.

let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.

Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as  you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.

\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-2\\ k=5\\ p=-1 \end{cases}\implies 4(-1)(y-5)=[x-(-2)]^2\implies -4(y-5)=(x+2)^2 \\\\\\ y-5=-\cfrac{1}{4}(x+2)^2\implies y=-\cfrac{1}{4}(x+2)^2+5

You might be interested in
Suppose a line parallel to side BC of triangle ABC intersects AB and AC at point D and E, respectively. Find the length of AE if
MrRissso [65]

Answer: AE=13

Step-by-step explanation: took test

4 0
3 years ago
Solve ninety two hundredths plus four and six tenths plus eight
stiks02 [169]
13.52 should be the correct answer
8 0
3 years ago
How do I do this homework???​
Nonamiya [84]

Step-by-step explanation:

a)

135

/ \

3. 45

/ \

3. 15

/ \

3. 5

b)

250

/ \

10 .25

/\ / \

2 5. 5 5

c)

351

/ \

3. 117

/ \

3. 39

/ \

3. 13

Hope it helps :)

5 0
4 years ago
8 is what percent of 24?
Irina18 [472]

Answer:

1, 33.3

2, 81.9

3, 240

4, the farmer sold 33.3 of his crops

5, 750 students are enrolled.

5 0
3 years ago
Read 2 more answers
-6p (p4- 8) what’s the answer ?
Helen [10]

Answer:

-6p^5+48p

Step-by-step explanation:

-6p (p^4- 8)= -6p^5+48p

5 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone help me with the top 1-3. Using similar figures subject
    8·1 answer
  • ed is using the recipe shown to make fruite salad 4 bananas diced 3 apples diced 6 pears diced 10 strawberries diced he wants to
    15·1 answer
  • Use the quadratic formula to solve x² + 7x + 8 = 0. What are the solutions to the equation? Round irrational solutions to the ne
    13·2 answers
  • How many times does 9 go into 143
    11·1 answer
  • PLEEEAAASSSSEEEE HEEEEEELLPP!!!! I WILL GIVE BRAINLIEST!!!!!!!!!
    12·1 answer
  • What is the step by step answer of 3 + 1 1/4=
    10·2 answers
  • The point slope equation for this slope is 2
    10·1 answer
  • Find the value of x<br> x=?
    10·1 answer
  • Fancy Nails charges $28 for a pedicure plus $9 for each treatment. Lara's Nails charges $22 for
    8·2 answers
  • HELP ASP SHOW UR WORK WILL GET BRAINILEST AND 10 points
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!