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Answer:
See attached diagram
Step-by-step explanation:
You are given the equation of hyperbola
From this equation,
- the center of hyperbola is at point (1,-3);
- the real semi-axes
- the imaginary semi-axes
Draw two parallel lines x=1 and y=-3 (they intersect at the center of hyperbola), then on horizontal line match two hyperbola's vertices (7 units to the left and 7 units to the right from the center). Then draw two branches of hyperbola (one in negative direction and one in positive direction).
Let the length of one of the shorter pieces be 
. Then, we know that two of the pieces are that length, and the third piece is 
. Since these are all pieces of a rope, all we need to do to figure out the lengths is add all those together, solve for , and then plug that back in to the desired lengths:
Shorter pieces:
Longer piece:
Shorter pieces:
Longer piece: