Standard forms of the equation of an ellipse with center (0,0)
The standard form of the equation of an ellipse with center
and major axis on the
x-axis is
where
the length of the major axis is
the coordinates of the vertices are
the length of the minor axis is
the coordinates of the co-vertices are
the coordinates of the foci are
, where
See
[link]a
The standard form of the equation of an ellipse with center
and major axis on the
y-axis is
where
the length of the major axis is
the coordinates of the vertices are
the length of the minor axis is
the coordinates of the co-vertices are
the coordinates of the foci are
, where
See
[link]b
Note that the vertices, co-vertices, and foci are related by the equation
When we are given the coordinates of the foci and vertices of an ellipse, we can use this relationship to find the equation of the ellipse in standard form.
(a) Horizontal ellipse with center
(b) Vertical ellipse with center
Given the vertices and foci of an ellipse centered at the origin, write its equation in standard form.
Determine whether the major axis lies on the
x - or
y -axis.
If the given coordinates of the vertices and foci have the form
and
respectively, then the major 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 major axis is the
y -axis. Use the standard form
Use the equation
along with the given coordinates of the vertices and foci, to solve for
Substitute the values for
and
into the standard form of the equation determined in Step 1.
Writing the equation of an ellipse centered at the origin in standard form
What is the standard form equation of the ellipse that has vertices
and foci
The foci are on the
x -axis, so the major axis is the
x -axis. Thus, the equation will have the form
The vertices are
so
and
The foci are
so
and
We know that the vertices and foci are related by the equation
Solving for
we have:
Now we need only substitute
and
into the standard form of the equation. The equation of the ellipse is
Can we write the equation of an ellipse centered at the origin given coordinates of just one focus and vertex?
Yes. Ellipses are symmetrical, so the coordinates of the vertices of an ellipse centered around the origin will always have the form
or
Similarly, the coordinates of the foci will always have the form
or
Knowing this, we can use
and
from the given points, along with the equation
to find
Writing equations of ellipses not centered at the origin
Like the graphs of other equations, the graph of an
ellipse can be translated. If an ellipse is translated
units horizontally and
units vertically, the center of the ellipse will be
This
translation results in the standard form of the equation we saw previously, with
replaced by
and
y replaced by
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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