Does an Elliptic Orbit's Speed Depend on Its Semi-Major Axis?

[fahd]

hi
i have this question to do which says..

*)A particle moves in a elliptic orbit under the influence of a central force F= -k/r^2.Prove that the product of the maximim and minimum speeds is equal to [2 pi a/t]^2 where 'a' is the semi major axis of the ellipse and 't' is the period of its motion..

Dont u think it should be the semi minor axis 'b' instead of the semi major axis 'a'..in the question..because I am getting the former as the right answer..
please help!

 

[emptymaximum]

wow. i have the exact same problem.
you can express the 'right answer' in terms of b
$$( \frac{2 \pi a} { \tau } )^2$$ eqs 1
recall:
$$\tau = \frac{2 A} {l}$$ eqs 2
where A is the area of an ellipse and is given by ╥ab
substituting 2 into 1 gives:
$$( \frac{2 \pi a} { \tau } )^2 = \frac{l^2} {b^2}$$