When an
ellipse is not centered at the origin, we can still use the standard forms to find the key features of the graph. When the ellipse is centered at some point,
we use the standard forms
for horizontal ellipses and
for vertical ellipses. From these standard equations, we can easily determine the center, vertices, co-vertices, foci, and positions of the major and minor axes.
Given the standard form of an equation for an ellipse centered at
sketch the graph.
Use the standard forms of the equations of an ellipse to determine the center, position of the major axis, vertices, co-vertices, and foci.
If the equation is in the form
where
then
the center is
the major axis is parallel to the
x -axis
the coordinates of the vertices are
the coordinates of the co-vertices are
the coordinates of the foci are
If the equation is in the form
where
then
the center is
the major axis is parallel to the
y -axis
the coordinates of the vertices are
the coordinates of the co-vertices are
the coordinates of the foci are
Solve for
using the equation
Plot the center, vertices, co-vertices, and foci in the coordinate plane, and draw a smooth curve to form the ellipse.
Graphing an ellipse centered at (
h ,
k )
Graph the ellipse given by the equation,
Identify and label the center, vertices, co-vertices, and foci.
First, we determine the position of the major axis. Because
the major axis is parallel to the
y -axis. Therefore, the equation is in the form
where
and
It follows that:
the center of the ellipse is
the coordinates of the vertices are
or
and
the coordinates of the co-vertices are
or
and
the coordinates of the foci are
where
Solving for
we have:
Therefore, the coordinates of the foci are
and
Next, we plot and label the center, vertices, co-vertices, and foci, and draw a smooth curve to form the ellipse.
Given the general form of an equation for an ellipse centered at (
h ,
k ), express the equation in standard form.
Recognize that an ellipse described by an equation in the form
is in general form.
Rearrange the equation by grouping terms that contain the same variable. Move the constant term to the opposite side of the equation.
Factor out the coefficients of the
and
terms in preparation for completing the square.
Complete the square for each variable to rewrite the equation in the form of the sum of multiples of two binomials squared set equal to a constant,
where
and
are constants.
Divide both sides of the equation by the constant term to express the equation in standard form.
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.