This question is from edexcel IAL paper c34 no.13
[hr][/hr]
13. A curve C has parametric equations:
. . . . .\(\displaystyle x\, =\, 6\, \cos(2t),\, y\, =\, 2\, \sin(t),\, \dfrac{\pi}{2}\, <\, t\, <\, \dfrac{\pi}{2}\)
(a) Show that \(\displaystyle \, \dfrac{dy}{dx}\, =\, \lambda\, \csc(t),\, \) giving the exact value of the constant \(\displaystyle \, \lambda.\)
(b) Find an equation of the normal to C at the point where \(\displaystyle \, t\, =\, \dfrac{\pi}{3}.\, \) 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
. . . . .\(\displaystyle x\, =\, f,\, k\, <\, y\, <\, k\)
where f (y) is a polynomial in y and k is a constant.
(c) Find f (y).
(d) State the value of k.
[HR][/HR]
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 by letting f=0. (which give k= 2^1/2
Is that using the range of f? How to find the range of f
BELOW IS THE ANSWER KEY.
Thank you very much!!!!!!!!!!!!!!!!
[hr][/hr]
13. A curve C has parametric equations:
. . . . .\(\displaystyle x\, =\, 6\, \cos(2t),\, y\, =\, 2\, \sin(t),\, \dfrac{\pi}{2}\, <\, t\, <\, \dfrac{\pi}{2}\)
(a) Show that \(\displaystyle \, \dfrac{dy}{dx}\, =\, \lambda\, \csc(t),\, \) giving the exact value of the constant \(\displaystyle \, \lambda.\)
(b) Find an equation of the normal to C at the point where \(\displaystyle \, t\, =\, \dfrac{\pi}{3}.\, \) 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
. . . . .\(\displaystyle x\, =\, f,\, k\, <\, y\, <\, k\)
where f (y) is a polynomial in y and k is a constant.
(c) Find f (y).
(d) State the value of k.
[HR][/HR]
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 by letting f=0. (which give k= 2^1/2
Is that using the range of f? How to find the range of f
BELOW IS THE ANSWER KEY.
Thank you very much!!!!!!!!!!!!!!!!
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