(558, #5) Find an equation of the tangent to the curve 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,

and when x=5 ,

At last,

Answer(b) :

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