Like the graphs for other equations, the graph of a hyperbola can be translated. If a hyperbola is translated
units horizontally and
units vertically, the center of the
hyperbola will be
This translation results in the standard form of the equation we saw previously, with
replaced by
and
replaced by
Standard forms of the equation of a hyperbola with center (
h ,
k )
The standard form of the equation of a hyperbola with center
and transverse axis parallel to the
x -axis is
where
the length of the transverse axis is
the coordinates of the vertices are
the length of the conjugate axis is
the coordinates of the co-vertices are
the distance between the foci is
where
the coordinates of the foci are
The asymptotes of the hyperbola coincide with the diagonals of the central rectangle. The length of the rectangle is
and its width is
The slopes of the diagonals are
and each diagonal passes through the center
Using the
point-slope formula , it is simple to show that the equations of the asymptotes are
See
[link]a
The standard form of the equation of a hyperbola with center
and transverse axis parallel to the
y -axis is
where
the length of the transverse axis is
the coordinates of the vertices are
the length of the conjugate axis is
the coordinates of the co-vertices are
the distance between the foci is
where
the coordinates of the foci are
Using the reasoning above, the equations of the asymptotes are
See
[link]b .
Like hyperbolas centered at the origin, hyperbolas centered at a point
have vertices, co-vertices, and foci that are related by the equation
We can use this relationship along with the midpoint and distance formulas to find the standard equation of a hyperbola when the vertices and foci are given.
Given the vertices and foci of a hyperbola centered at
write its equation in standard form.
Determine whether the transverse axis is parallel to the
x - or
y -axis.
If the
y -coordinates of the given vertices and foci are the same, then the transverse axis is parallel to the
x -axis. Use the standard form
If the
x -coordinates of the given vertices and foci are the same, then the transverse axis is parallel to the
y -axis. Use the standard form
Identify the center of the hyperbola,
using the midpoint formula and the given coordinates for the vertices.
Find
by solving for the length of the transverse axis,
, which is the distance between the given vertices.
Find
using
and
found in Step 2 along with the given coordinates for the foci.
Solve for
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.