And where does it come from? Possible clues are Cuch's obsessions: Joyce, Russians, numerics, exp(5),...Iceland? But most likely the title of the thread. To get [$]y[$] appearing as a linear and a trig term suggests something involving both triangles and circles...And why have [$]x[$] and [$]\epsilon[$] and not just the numbers? These questions are so much more interesting than 0.964... I'm afraid.
Actually ...these are the things to do for relaxation
I have deliberately scoped the problem to work with numbers for the moment, to focus the mind.
ppauper gets an A+ for solving the (initial) problem. We can build on his solution (I see about 7 other solutions offhand). One small question is when the eccentricity [$]\varepsilon > 1.[$]
The answer is in the stars
As ppauper says: It is developing skill to answer the question that is posed.