SRJC/I/Q9 Applications of Differentiation

(a) A curve C is defined by the equation xy + y² – x³ = 7.

Find the coordinates of the point where the tangent line to the curve C is parallel to the y-axis and state the equation of this tangent line.

(b) A curve is defined parametrically by the equations .

The fixed point P on the curve has parameter p. Find the equation of the normal to the cure at the point P, leaving your answer in terms of a and p. 

Given that the normal at point P does not meet the curve again, find exactly the range of values of p. 

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