39Radius vector is a vector starting at the center of coordinates and ending at some point of ellipse.
show thet the length of the radius vector of the ellipse x2a2+y2b2=1 drawn in the direction making an angle θ with the positive directtion of x-axis is √(a2b2b2cos2θ+a2sinθ)
Also show that the sum of the reciprocals of the squares is contant of any two semi-diameters of an ellipse which are at right angles to one another is constant.
what is radius vector of the ellipse ??????
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10 Answers
39
66@johny,
The center of coordinates is NOT the focus but the center of the ellipse itself.
39its not always the case.. i had read otherwise in many articles before
39i have taken the keppler laws as my base and you being a physics professor should be knowing what as i said
anyways i am not completely sure about my clainin maths
but AS FAR AS THE PHYSICS I HAVE READ, the center of coordinates IS THE focus of the ellipse
1@johny,
centre of coordinate is the centre of ellipse not the focus as far as i know
CENTRE OF ELLIPSE IS NOT D FOCUS
i think that onli kayamat sir wanted to say
1i got the answer
i hav taken a vector from d centre of ellipse which is the centre of coordinates in this particular case to any point of the ellipse
but what would i do if the equation is not in the standard formsuppose the origin is shifted
then,
in that case what would be the radius vector of the ellipse
should i take it from the origin of coordinate syastem or from the centre of the ellipse
PLEAZZZ REPLY IF ANYONE HA ANY SORT OF IDEA ABOUT THIS
1but what would i do if the equation is not in the standard formsuppose the origin is shifted
then,
in that case what would be the radius vector of the ellipse
should i take it from the origin of coordinate syastem or from the centre of the ellipse
PLEAZZZ REPLY IF ANYONE HA ANY SORT OF IDEA ABOUT THIS
66@johny
usually in polar coordinates, the conic sections are specified by giving the distance of a point from the focus. However, in the present case, the radius vector is measured relative to the center of coordinates.
As far as the problem is concerned, proceed as follows:
Any point on the ellipse is of the form (a cos t, b sin t). Here t is eccentric angle. As such the radius vector is r = √a2 cos2t + b2 sin2 t. Next, we notice that
tan θ = b sin ta cos t = ba tan t
which gives us
tan t = ab tan θ.
As such we have
cos2 t = 11+tan2 t = b2b2 + a2 tan2θ = b2 cos2θb2 cos2θ + a2 tan2θ
And
sin2t = tan2t1+tan2 t = a2 sin2θb2 cos2θ + a2 tan2θ
Hence,
r = √a2 b2b2 cos2θ + a2 tan2θ
as required.
1but from where should i take the radius vector
from the centre of coordinates
or
from the centre of coordinate system
or
from the focus
if it is not in the standard form