Hello, sweetG!
a) Find the equation of the normal to where
When
We have: .
When , the slope of the tangent is: .
. . Hence, the slope of the normal is:
The equation of the normal is: .
b) This normal cuts the coordinate axis at P and Q.
Given that P and Q are adjacent vertices of a rhombus,
and that the diagonals of this rhombus intersect at the origin,
determine the area of this rhombus.
The intercept of the normal are: .
If the diagonals intersect at the origin, the rhombus looks like this: Code:

Q o (0,11/6)
*  *
*  *
R *  * P
   o      +      o   
(11/9,0) *  * (11/9,0)
*  *
*  *
S o (0,11/6)

The area of a rhomus is onehalf the product of its diagonals.
The horizontal diagonal has length: .
The vertical diagonal has length: .
The area is: .
*