Given the equation of a hyperbola in standard form, locate its vertices and foci.
Determine whether the transverse axis lies on the
x - or
y -axis. Notice that
is always under the variable with the positive coefficient. So, if you set the other variable equal to zero, you can easily find the intercepts. In the case where the hyperbola is centered at the origin, the intercepts coincide with the vertices.
If the equation has the form
then the transverse axis lies on the
x -axis. The vertices are located at
and the foci are located at
If the equation has the form
then the transverse axis lies on the
y -axis. The vertices are located at
and the foci are located at
Solve for
using the equation
Solve for
using the equation
Locating a hyperbola’s vertices and foci
Identify the vertices and foci of the
hyperbola with equation
The equation has the form
so the transverse axis lies on the
y -axis. The hyperbola is centered at the origin, so the vertices serve as the
y -intercepts of the graph. To find the vertices, set
and solve for
The foci are located at
Solving for
Therefore, the vertices are located at
and the foci are located at
Just as with ellipses, writing the equation for a hyperbola in standard form allows us to calculate the key features: its center, vertices, co-vertices, foci, asymptotes, and the lengths and positions of the transverse and conjugate axes. Conversely, an equation for a hyperbola can be found given its key features. We begin by finding standard equations for hyperbolas centered at the origin. Then we will turn our attention to finding standard equations for hyperbolas centered at some point other than the origin.
Hyperbolas centered at the origin
Reviewing the standard forms given for hyperbolas centered at
we see that the vertices, co-vertices, and foci are related by the equation
Note that this equation can also be rewritten as
This relationship is used to write the equation for a hyperbola when given the coordinates of its foci and vertices.
Given the vertices and foci of a hyperbola centered at
write its equation in standard form.
Determine whether the transverse axis lies on the
x - or
y -axis.
If the given coordinates of the vertices and foci have the form
and
respectively, then the transverse axis is the
x -axis. Use the standard form
If the given coordinates of the vertices and foci have the form
and
respectively, then the transverse axis is the
y -axis. Use the standard form
Find
using the equation
Substitute the values for
and
into the standard form of the equation determined in Step 1.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.