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
babymother [125]
3 years ago
12

The center of a hyperbola is (−4,3) , and one vertex is (−4,7) . The slope of one of the asymptotes is 2.

Mathematics
2 answers:
Monica [59]3 years ago
7 0

Answer:

The answer to your question is below

Step-by-step explanation:

C (-4, 3)

V (-4, 7)

asymptotes = 2 = \frac{b}{a}

- This is a vertical hyperbola, the equation is

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

slope = 2

a is the distance from the center to the vertex = 4

b = 2(4) = 8

       \frac{(y - 3)^{2} }{4^{2} } + \frac{(x + 4)^{2} }{8^{2} } = 1

       \frac{(y - 3)^{2} }{16} + \frac{(x + 4)^{2} }{64} = 1

Ne4ueva [31]3 years ago
5 0

Answer:

\frac{(x+4)^{2}}{4} - \frac{(y-3)^{2}}{16} = 1

Step-by-step explanation:

The hyperbola centered at (h,k) has the following expression:

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

Where a and b are the length of the horizontal and vertical semi-axes, respectively.

Since the center and one vertex share the same vertical component (x=-4), it is easy to conclude that hyperbola has a vertical configuration (b > a). The distance between the center and the known vertex is equal to the length of the vertical semi-axis. Therefore:

b = 4

The slope of the hyperbola is given by the following relationship:

\frac{b}{a} = 2

The length of the horizontal semi-axis is:

a = \frac{b}{2}

a = 2

The standard form of the equation of the hyperbola is:

\frac{(x+4)^{2}}{4} - \frac{(y-3)^{2}}{16} = 1

You might be interested in
Help asap!!!!!!!!!!!!!!!!!!!!!!! 20 points!1
Darya [45]

Answer:

24

Step-by-step explanation:

8 0
2 years ago
Plz helpppppp me with this question​
jarptica [38.1K]

Answer:

R L Q

Step-by-step explanation:

Im pretty sure thats right sorry if Its not

4 0
3 years ago
Read 2 more answers
A block of copper weighs 2160g and has a volume of 240cm cubed. what is the density of the copper?
mrs_skeptik [129]
(Mass) 2160g (Divided by) / (Volume) 240cm (Equals) = 9 (Density)

3 0
2 years ago
What is the name of the symbol used to denote square root?
kiruha [24]
I believe the term is a "radical"
Hope this helps!
3 0
2 years ago
Read 2 more answers
PLEASE HELP! 40 POINTS! All the problems are in the screenshot!
alisha [4.7K]
1.
Domain: {-1, 0, 2, 3}
Range: {2, 4, 6}

2.
Ax+By=C: linear equation standard form
y=mx+b: slope intercept form
(y-y^1)=m(x-x^1): point slope form
5 0
2 years ago
Other questions:
  • Lowest term 2/11÷5 ​
    12·1 answer
  • What is the difference between integers and real numbers?
    9·1 answer
  • Type the correct answer in the box
    10·1 answer
  • A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 42 states. What is the probability that sh
    11·1 answer
  • If a polygon (with n sides) has three obtuse angles, what could n be? Show clear workings and provide an explanation.
    12·1 answer
  • How do you do inequalities
    14·1 answer
  • The speed of light is 1.86 x 105 miles per second. What is this number in standard notation?
    7·2 answers
  • Suppose that 40% of cars in your area are manufactured in the U.S., 30% in Japan, 10% in Germany, and 20% in other
    12·1 answer
  • What is the variable in this expression? 5x^2 + x+7
    14·1 answer
  • Tiffany sees this given dilation and claims that the scale factor is 2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!