ellipse- k c sinha

Radius vector is a vector starting at the center of coordinates and ending at some point of ellipse.

its not always the case.. i had read otherwise in many articles before

i 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

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

@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 tan²Î¸ = b² cos²Î¸b² cos²Î¸ + a² tan²Î¸
And
sin²t = tan²t1+tan² t = a² sin²Î¸b² cos²Î¸ + a² tan²Î¸

Hence,
r = √a² b²b² cos²Î¸ + a² tan²Î¸
as required.

but 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