Relativistic mechanics:circle becoming ellipse.

[sudipmaity]

Homework Statement

Suppose a circle of radius 'b' is set in motion.Calculate the relativistic speed parameter β(=v/c) such that the circle is seen as an ellipse of semiminor axis 'a' and semimajor axis 'b' where a <b.3 marks.

Homework Equations

L=L₀/γ

The Attempt at a Solution

Whichever direction the circle travels say x-axis the radius shrinks in that direction to 'a'.
So a=b/γ.
(a/b)²=1-(v/c)²
β=√[1-(a/b)²]
Is my deduction correct? Do I need to show more mathematics here or to say is my above workout enough?

 

[Orodruin]

Looks fine to me. I would say "becomes length contracted" rather than "shrinks" though.