The longest and the shortest distance of a planet from the sun are `R_(1)` and `R_(2)`. Distances from sun when it is normal to major axis of orbit is

Options

A. `(R_(1)+R_(2))/2`
B. `sqrt((R_(1)^(2)+R_(2)^(2))/2)`
C. `(R_(1)R_(2))/(R_(1)+R_(2))`
D. `(2R_(1)R_(2))/(R_(1)+R_(2))`

Answer

D

Explanation

`R_(1)=(1+e)a, R_(2)=(1-e)a`
`a=(R_(1)+R_(2))/2,R_(1)R_(2)=(1-e^(2))a^(2)`
since semi-latus rectum `=(b^(2))/a`
`=(a^(2)(1-e^(2)))/(a)=(R_(1)R_(2))/((R_(1)+R_(2))/2)=(2R_(1)R_(2))/(R_(1)+R_(2))`