This question is from edexcel IAL paper c34 no.13

**13.** A curve *C* has parametric equations:

. . . . .[tex]x\, =\, 6\, \cos(2t),\, y\, =\, 2\, \sin(t),\, -\dfrac{\pi}{2}\, <\, t\, <\, \dfrac{\pi}{2}[/tex]

(a) Show that [tex]\, \dfrac{dy}{dx}\, =\, \lambda\, \csc(t),\, [/tex] giving the exact value of the constant [tex]\, \lambda.[/tex]

(b) Find an equation of the normal to *C* at the point where [tex]\, t\, =\, \dfrac{\pi}{3}.\, [/tex] Give you answer in the form *y* = *mx* + *c*, where *m* and *c* are simplified surds.
The cartesian equation for the curve *C* can be written in the form

. . . . .[tex]x\, =\, f(y),\, -k\, <\, y\, <\, k[/tex]

where *f* (*y*) is a polynomial in *y* and *k* is a constant.

(c) Find *f* (*y*).

(d) State the value of *k*.

My problem is part (d) where the answer is k= - 2 but I don't know how to find it. (WHY is NEGATIVE?)

I cannot solve f(y) by letting f(y)=0.

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