ok, the most common possible methods of doing parametrics are:
1. make the parameter the subject in one of the two given equations (x- and y- eqns) and substitute that to the other one
If it can't be done easily,
2. square one of the given eqns or square both of them and look for some patterns, and rearrange the squared thing if necessary. OR
3. rearrange one or both of the eqns and look for patterns
for (a):
you can sort of see that x^2 will contain some terms in the y expression.
x^2 = t^2 + 1/t^2 + 2(t)(1/t), so x^2 = y + 2
for (b):
you cant really make t the subject in either eqns (u can, but it wont look really nice)
theres a similarity between "1 + 2^-t" and "2^t" in that they both have ^t
you can write "1 + 2^-t" as "1 + 1/2^t" so this becomes "1 + 1/y"
so, x = 1 + 1/y and depending on the level of the question (reflected in the number of marks and in the school or textbook that set it) you may need to write this as xy = y + 1 which becomes y (x-1) = 1 which becomes y = 1/(x-1)
another question for practice:
express in cartesian form: x = 2cos@ and y = 1/2 sin@
hint: use Pythagorean identity
