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
aksik [14]
3 years ago
8

Which is the equation of a hyperbola with directrices at y = ±2 and foci at (0, 4) and (0, −4)?

Mathematics
1 answer:
Advocard [28]3 years ago
4 0

Answer:

Step-by-step explanation:

First off, I'm assuming that when you said "directrices" you mean the oblique asymptotes, since hyperbolas do not have directrices they have oblique asymptotes.

If we plot the asymptotes and the foci, we see that where the asymptotes cross is at the origin. This means that the center of the hyperbola is (0, 0), which is important to know.

After we plot the foci, we see that they are one the y-axis, which is a vertical axis, which means that the hyperbola opens up and down instead of sideways. Knowing those 2 characteristics, we can determine that the equation we are trying to fill in has the standard form

\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1

We know h and k from the center, now we need to find a and b. Those values can be found from the asymptotes. The asymptotes have the standard form

y = ±\frac{a}{b}(x-h)+k

Filling in our asymptotes as they were given to us:

y = ±\frac{2}{1}(x-0)+0 where a is 2 and b is 1. Now we can write the formula for the hyperbola!:

\frac{(y-0)^2}{4}-\frac{(x-0)^2}{1}=1 which of course simplifies to

\frac{y^2}{4}-\frac{x^2}{1}=1

You might be interested in
Shari bought 3 breath mints and received $2.76 change.Jamal bought 5 breath mints and received $1.20 change. If Shari and Jamal
vekshin1

Answer:

                                     

Step-by-step explanation:

8 0
2 years ago
PLS HELP ASAP! GIVING BRAINLY
ioda
The answer would be (x+1) and (x+10) so E
4 0
2 years ago
Read 2 more answers
Find the area of the trapezoid
katovenus [111]

Answer: 49 in^2

Step-by-step explanation:

Trapezoid area formula = (a+b/2) x h

So...

(5+9/2) x 7

= 49 in^2

4 0
2 years ago
Read 2 more answers
In a vegetable garden,1/4 of the plants are peppers. of the pepper plants ,1/3 are yellow peppers. what fraction of the plants a
max2010maxim [7]
Given that 1/4 of the plants in the garden are peppers, and 1/3 of the 1/4 pepper plants are yellow peppers, we could get the fraction of the yellow peppers by multiplying 1/4 by 1/3. And we get the answer 1/12. Therefore, 1/12 is the fraction of yellow peppers.
6 0
3 years ago
(x^(2)-4x+3)(-3x^(2)+7x-1)<br><br> Multiply Express your answer in simplest form.
iren [92.7K]

The answer is 42^3 from your question

7 0
3 years ago
Other questions:
  • Some researchers have conjectured that stem-pitting disease in peach tree seedlings might be controlled with weed and soil treat
    9·1 answer
  • What goes into 80 and 11
    14·1 answer
  • Look at the picture please help
    9·2 answers
  • There are 5 cars and 7 trucks in a parking lot. James says that 50% are cars . do you agree or disagree with James
    13·1 answer
  • Find the area of the regular polygon below. PLEASE HELP WILL MARK BRAINLIEIST!
    5·2 answers
  • Can anyone help me w this acellus question
    13·2 answers
  • Someone help meee I hate my teacher she asssign nvm I’m not even gonna say
    13·2 answers
  • PLEASE HELP ME ITS FOR A QUIZ!
    15·1 answer
  • Pls help hella lost
    8·1 answer
  • Find volume of this figure
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!