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C4 Differentiation and parametric equations, need help!

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Need help with Q5b and Q8D. I can do the first part of the question but I'm totally lost on this part :frown:
Reply 1
Original post by Shiv Loves Maths
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Need help with Q5b and Q8D. I can do the first part of the question but I'm totally lost on this part :frown:


For Q8 d, you can either find the Cartesian equation of the curve and solve simultaneously, or you can substitute the expressions for x and y in the equation of the normal and solve it simultaneously that way. I'd go for the second method as finding the Cartesian equation here seems pointless since it doesn't ask you to do it specifically anywhere.
You would do 5b in the same way.
(edited 7 years ago)
Original post by B_9710
For Q8 d, you can either find the Cartesian equation of the curve and solve simultaneously, or you can substitute the expressions for x and y in the equation of the normal and solve it simultaneously that way. I'd go for the second method as finding the Cartesian equation here seems pointless since it doesn't ask you to do it specifically anywhere.
You would do 5b in the same way.


Coukd you do it for me please?
Reply 3
Original post by Shiv Loves Maths
Coukd you do it for me please?


I won't do it all. But I'll point you in the right direction.
We have the equation of the normal at A as
6y16x+23=0 6y-16x+23=0
But we know that x=4cos2t and y=3sint x=4\cos 2t \text{ and } y=3\sin t so if we substitute these expressions in for x and y in the equation of the the normal we can find the t values and the point of intersection of the normal and the curve.
So 6(3sint)16(4cos2t)+23=0 6(3\sin t) -16(4\cos 2t) +23=0 .
cos2t=12sin2t \cos 2t = 1-2\sin^2 t so now use this to form a quadratic in sint \sin t and then solve. Remember that you already know that sint=1/2 \sin t = 1/2 so you already know one of the factors of the quadratic so it should be very easy to find the other and then solve.

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