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
FromTheMoon [43]
3 years ago
6

Derive the equation of the parabola with a focus at (6,2) and a directrix of y=1

Mathematics
1 answer:
Nataly [62]3 years ago
4 0
If the focus is at (6, 2) and the directrix is a horizontal line y = 1, then that tells us that is an x^2 parabola.  Since the parabola hugs the focus, it will open upwards since the focus is above the directrix.  The rule here is that the vertex is the same distance from the focus as it is from the directrix.  If the focus is at a y-value of 2 and the directrix is at y = 1, then the vertex is right in between them as far as the y coordinate goes, which is 1.5.  It will have the same x coordinate at the focus.  The vertex is in the form (h, k), so our h is 6, and our k is 1.5.  The vertex is (6, 1.5).  The standard form of a parabola of this type is (x-h)^2=4p(y-k), where p is the distance from the vertex to the focus.  Our p is 1/2.  Using the h and k from the vertex, and the p of 1/2, we now have this as our equation, not yet simplified: (x-6)^2=4( \frac{1}{2})(y-1.5).  That will simplify a bit to (x-6)^2=2(y-1.5).  Depending upon how you are to state your answer, how it needs to "look" in the end will vary.  I am going to FOIL the left and distribute the right and then put everything on one side and set it equal to y.  That would be this: \frac{1}{2}( x^{2} -12x+39)=y.  And there you go!
You might be interested in
1.5÷5.46 show your work
arlik [135]

Answer:

0.274725275

Step-by-step explanation:

(1.5)/(5.46)

4 0
3 years ago
Can anyone help me?<br><br>Find the exact variable.<br><br>Thank you so much!​
sdas [7]
I think this is right
a = 8
b = 8
c = 5
d = 9
3 0
3 years ago
I need help with 9-12 ASAP<br> its due tomorrow.
mixas84 [53]
9) yes it is similar : it does not have to be congruent
10) scale factor: 2 (inside) :3 (outside)
11) ratio:  16 (inside) : 24 (outside)
12) Yes they are similar

hope this helps
7 0
3 years ago
50 points!!!! What is the area of the trapezoid​
Deffense [45]

Answer:

308 square feet

Step-by-step explanation:

A = 1/2 (26+18) (14)

A = 1/2 (44) (14)

A = 308

Answer

308 square feet

4 0
2 years ago
Read 2 more answers
HELP
3241004551 [841]
This might be the answer but I no sure

8 0
2 years ago
Other questions:
  • Write an expression that is equal to 3× 2 1/4
    5·2 answers
  • Help please? Brainliest and points!
    11·2 answers
  • Prove algebraically what type of function this is (even, odd, or neither).
    6·1 answer
  • Determine the distance between two points p(3,4) q(4,5)
    9·1 answer
  • A. The GCF of 18 and 21 is__
    6·1 answer
  • Please help me answer this
    10·1 answer
  • Pls help, <br><br> 6(d+1)−2d=54
    8·1 answer
  • Put these in order starting from the smallest 6^2,3^4,2^5,5^3
    10·1 answer
  • You have a total of 80 dollars to spend on groceries. You spend some money on meat and then spend 52 dollars on everything else.
    12·2 answers
  • the total cost of a pair of shoes is $85.86. What was the cost of the shoes before the 8% sales tax was added?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!