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Pure Maths A2


Reebz.F
Posts: 42
Topic starter
(@reebz-f)
Eminent Member
Joined: 2 years ago

 

image

Hello.

Does anyone know how to do this question?

I have tried it but keep getting the wrong answers.

6 Replies
MaxiMaxi
(@maximaxi)
Joined: 2 years ago

Eminent Member
Posts: 48

@reebz-f

whats the correct value for r? I’ve got an answer but I don’t want to show my working out if it’s wrong 

 

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Reebz.F
(@reebz-f)
Joined: 2 years ago

Eminent Member
Posts: 42

@maximaxi For part a you get :

y^2=(9/4)x^2(4-x)^2

and for part b), r=10/3

 

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Zubair
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(@zubair)
Joined: 2 years ago

Eminent Member
Posts: 41

@reebz-f

Hi there reebz,

in part a you would work out what y^2 is and what x^2 is from the information you have - as the answer is in terms of them. Then to combine those two equations together you need to play around with some identities. I change y^2 = 9sin^2(2t) into 9(1-cos^2(2t)) then worked out what cos(2t) was in terms of x as cos(2t) = 1 - 2sin^2(t). 

for part b, you plug in the y^2 formula into the equation of a circle x^2 + y^ = r^2 (as they intersect, we can do simultaneous equations). Once you’ve got an expression for that, c1 intersects c2 such that the radius is as big as possible - hence it only touches 4 times. This means we should make dr/dx = 0 and solve it to get a maximum r value.

click the spoiler if you want to see my solution

Spoiler
Solution
E070E614 2CDC 4622 8871 BC6C136FE226

 [/spoiler]

 

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Zubair
Admin
(@zubair)
Joined: 2 years ago

Eminent Member
Posts: 41

Sorry @maximaxi you were too slow ? 

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MK
 MK
(@mk)
Joined: 1 week ago

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Posts: 1

@maximaxi sorry what paper is this

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Reebz.F
Posts: 42
Topic starter
(@reebz-f)
Eminent Member
Joined: 2 years ago

@Zubair

Hello.

Thank you so much for this,the explanations were so helpful and I understand how to do the question now.

Thank you!

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