Answer:

Step-by-step explanation:
The given parametric equation is;

<h3>
<u>BY ELIMINATING THE PARAMETER</u></h3>
To eliminate the parameter we make
the subject in one equation and put it inside the other.
We make
the subject in
because it is easier.
Or
We now substitute this into
.
This gives us;
.
.
We have now eliminated the parameter.
The equation of the tangent at (6,4) is given by;

where the gradient function is given by;

We substitute
into the gradient function to obtain the gradient.



The equation of the tangent becomes

We simplify to obtain


<h3><u>WITHOUT ELIMINATING THE PARAMETER</u></h3>
The given parametric equation is;

For 

For 

The slope is given by;



At the point, (6,4), we plug in any of the values into the parametric equation and find the corresponding value for
.
Notice that
When
, 




when
, 



But the slope is the same when we plug in any of these values for t.

The equation of the tangent becomes

We simplify to obtain

