,
where 
and 
correspond to the values of x(t) and y(t) at some point t.
at the point (5, 3) by two methods :
a) without eliminating the parameter;
b) by first eliminating the parameter;
Solution (a) :
The equation of the tangent has the form
,
where
and
correspond to the values of x(t) and y(t) at some point t.
To find this point we need to solve the equation 2t+3 = 5. It follows that t = 1.
Now,
and
Thus 
and we have 
Answer(a) : 
Solution (b) :
From the expression for x(t) we have
.
Substituting it in the 
we get
Now,
At last,
Answer(b) : 
by es