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Parametric equations questions? Watch

1. Hi, I've been doing some work on parametric equations and I have a few questions which I'm stuck on. I would appreciate any help given!

With Q3b, is there are way of completing the question without finding the cartesian equation (or is it a necessary step?). And I'm not too sure what I should do next, as I can't factorise it.

For Q4c, I think my working out so far is correct (parts a/b are correct) but I don't see how I can prove PA=2BP as they're in different forms.

2. (Original post by Bazinga?)
With Q3b, is there are way of completing the question without finding the cartesian equation (or is it a necessary step?). And I'm not too sure what I should do next, as I can't factorise it.
Yes. In the equation of the tangent, (is it x+3y-4=0 ?) replace x with t^3 and y with t^2 to get a cubic in t. You know that t=-2 is a repeated root so finding the other root should be easy.
3. (Original post by BabyMaths)
Yes. In the equation of the tangent, (is it x+3y-4=0 ?) replace x with t^3 and y with t^2 to get a cubic in t. You know that t=-2 is a repeated root so finding the other root should be easy.
Oh okay, by doing what you said, I got the right answer. However, I don't understand why you substitute the t's back into the equation of the tangent? And how do you know t=-2 is a repeated root?

Also, I know it's more long winded, but if I found the cartesian equation of the curve and equated that to the tangent, would that find t?
4. (Original post by Bazinga?)
Hi, I've been doing some work on parametric equations and I have a few questions which I'm stuck on. I would appreciate any help given!

With Q3b, is there are way of completing the question without finding the cartesian equation (or is it a necessary step?). And I'm not too sure what I should do next, as I can't factorise it.

For Q4c, I think my working out so far is correct (parts a/b are correct) but I don't see how I can prove PA=2BP as they're in different forms.

For 3)

sub and multiply by 3

factorizing by pair

factorizing

and here is the repeated root and the other one.

An other method maybe the long division by (t+2) because you know
that one of the roots is -2 (where the tangent meets the curve)
5. (Original post by ztibor)
For 3)

sub and multiply by 3

factorizing by pair

factorizing

and here is the repeated root and the other one.

An other method maybe the long division by (t+2) because you know
that one of the roots is -2 (where the tangent meets the curve)
Okay, thank you for your help Would you be able to help with 4?
6. (Original post by Bazinga?)
Okay, thank you for your help Would you be able to help with 4?
Prove that

for c)
7. (Original post by ztibor)
Prove that

for c)
Thanks for your help, it is very much appreciated!

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