First, we rewrite the conic in standard form by multiplying the numerator and denominator by the reciprocal of 2, which is
Because
so we will graph a
hyperbola with a focus at the origin. The function has a
term and there is a subtraction sign in the denominator, so the directrix is
The directrix is
Plotting a few key points as in
[link] will enable us to see the vertices. See
[link] .
First, we rewrite the conic in standard form by multiplying the numerator and denominator by the reciprocal of 5, which is
Because
so we will graph an
ellipse with a
focus at the origin. The function has a
and there is a subtraction sign in the denominator, so the
directrix is
The directrix is
Plotting a few key points as in
[link] will enable us to see the vertices. See
[link] .
Defining conics in terms of a focus and a directrix
So far we have been using polar equations of conics to describe and graph the curve. Now we will work in reverse; we will use information about the origin, eccentricity, and directrix to determine the polar equation.
Given the focus, eccentricity, and directrix of a conic, determine the polar equation.
Determine whether the directrix is horizontal or vertical. If the directrix is given in terms of
we use the general polar form in terms of sine. If the directrix is given in terms of
we use the general polar form in terms of cosine.
Determine the sign in the denominator. If
use subtraction. If
use addition.
Write the coefficient of the trigonometric function as the given eccentricity.
Write the absolute value of
in the numerator, and simplify the equation.
Finding the polar form of a vertical conic given a focus at the origin and the eccentricity and directrix
Find the polar form of the
conic given a
focus at the origin,
and
directrix
The directrix is
so we know the trigonometric function in the denominator is sine.
Because
so we know there is a subtraction sign in the denominator. We use the standard form of
Finding the polar form of a horizontal conic given a focus at the origin and the eccentricity and directrix
Find the
polar form of a conic given a
focus at the origin,
and
directrix
Because the directrix is
we know the function in the denominator is cosine. Because
so we know there is an addition sign in the denominator. We use the standard form of
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
Got questions? Join the online conversation and get instant answers!