question_answer

Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle \[csa\]is\[\frac{1}{4}\]the area of the ellipse. (See figure) With db as the semi major axis, and ca as the semi minor axis. If \[{{t}_{1}}\]is the time taken for planet to go over path \[abc\] and \[{{t}_{2}}\]for path taken over \[cda\] then:          [JEE ONLINE 09-04-2016]

A)        \[{{t}_{1}}=3{{t}_{2}}\]

B)  \[{{t}_{1}}={{t}_{2}}\]

C)  \[{{t}_{1}}=2{{t}_{2}}\]

D)                   \[{{t}_{1}}=4{{t}_{2}}\]

Correct Answer: A

Solution :

[a] Total area = A

Area of sabc

Area of sadc