Lychee628
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The parametric equations of the curve C are x=at^2 and y=2at, where a is a postive constant. The points P and Q lie on C and have parameters p and q respectively.
a)Simplifying your answer in each case find
i)The gradient of the tangent to C at the the point P (Which i have done and got 1/p)
ii)The equation of the tangent to C at the point P(Which i have done and got yp-x-ap^2=0)

b)i)Find an expression, in its simplest form, for the gradient of the line PQ.
ii)Explain how you could use the answer of (b)(i) to derive the gradient of the tangent to C at the point P.

Can someone help solve part b i) and b ii)
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Lychee628
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Someone?
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Lychee628
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Bump...
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Lychee628
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??
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TeeEm
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(Original post by Ayaz789)
The parametric equations of the curve C are x=at^2 and y=2at, where a is a postive constant. The points P and Q lie on C and have parameters p and q respectively.
a)Simplifying your answer in each case find
i)The gradient of the tangent to C at the the point P (Which i have done and got 1/p)
ii)The equation of the tangent to C at the point P(Which i have done and got yp-x-ap^2=0)

b)i)Find an expression, in its simplest form, for the gradient of the line PQ.
ii)Explain how you could use the answer of (b)(i) to derive the gradient of the tangent to C at the point P.

Can someone help solve part b i) and b ii)
Let P(ap2,2ap) and Q(aq2,2aq)
find the gradient of the chord
then let q tend to p, ie set q=p
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Lychee628
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(Original post by TeeEm)
Let P(ap2,2ap) and Qaq2,2aq)
find the gradient of the chord
then let q tend to p, ie set q=p
I still dont understand it sorry :/
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TeeEm
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(Original post by Ayaz789)
I still dont understand it sorry :/
do you know how to find the gradient of 2 points if you have their coordinates?
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Lychee628
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(Original post by TeeEm)
do you know how to find the gradient of 2 points if you have their coordinates?
Yes you do y2-y1/x2-x1 but we dont have them in integer form? Or am i just acting ******ed
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TeeEm
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(Original post by Ayaz789)
Yes you do y2-y1/x2-x1 but we dont have them in integer form? Or am i just acting ******ed
what integer form?
If the points P and Q lie on the parabola with parametric equations

x = at2 y = 2at

then
t = p (say) at P and t = q at Q
You can find he gradient of PQ for:
P(ap2,2ap) and Q(aq2,2aq)
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Lychee628
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(Original post by TeeEm)
what integer form?
If the points P and Q lie on the parabola with parametric equations

x = at2 y = 2at

then
t = p (say) at P and t = q at Q
You can find he gradient of PQ for:
P(ap2,2ap) and Q(aq2,2aq)
What im saying is dont you have to do 2aq-2ap/aq^2-ap^2 ?? How would i do that? And would it not be 1 considering p & q are the same? Im sorry because i dont understand you
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TeeEm
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(Original post by Ayaz789)
What im saying is dont you have to do 2aq-2ap/aq^2-ap^2 ?? How would i do that? And would it not be 1 considering p & q are the same? Im sorry because i dont understand you
no
first find a simplified expression for the gradient, assuming P and Q are distinct points
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Lychee628
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(Original post by TeeEm)
no
first find a simplified expression for the gradient, assuming P and Q are distinct points
And how would i do that without y2-y1/x2-x1?
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TeeEm
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(Original post by Ayaz789)
And how would i do that without y2-y1/x2-x1?
of course with it!
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Lychee628
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(Original post by TeeEm)
of course with it!
Thats what i said before lol? What values would i use though? You said simplified?
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TeeEm
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(Original post by Ayaz789)
Thats what i said before lol? What values would i use though? You said simplified?
please read post 9 again carefully
then find the gradient PQ
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Lychee628
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(Original post by TeeEm)
please read post 9 again carefully
then find the gradient PQ
Im sorry but i dont understand it:/ that is a past paper question so can you please tell me how to get 4 marks on b i) and bii)
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Louisb19
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(Original post by Ayaz789)
Im sorry but i dont understand it:/ that is a past paper question so can you please tell me how to get 4 marks on b i) and bii)
 \dfrac{\mathrm{d}y}{\mathrm{d}x} (x_1 - x_2) = y_1 - y_2

Since we have defined a general point P (the parametric equations) on the curve, we can sub these values as  x_1 and  y_1 or  x_2 and  y_2 .

On a side note, it would be best if you could at least attempt the question. TeeEm does not take kindly to people just asking for answers
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Lychee628
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(Original post by Louisb19)
 \dfrac{\mathrm{d}y}{\mathrm{d}x} (x_1 - x_2) = y_1 - y_2

Since we have defined a general point P (the parametric equations) on the curve, we can sub these values as  x_1 and  y_1 or  x_2 and  y_2 .

On a side note, it would be best if you could at least attempt the question. TeeEm does not take kindly to people just asking for answers
Ohh okay ill attempt the question, and ill tell you within 10 minutes if i can do it or not Anyways thanks louis
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Lychee628
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(Original post by Louisb19)
 \dfrac{\mathrm{d}y}{\mathrm{d}x} (x_1 - x_2) = y_1 - y_2

Since we have defined a general point P (the parametric equations) on the curve, we can sub these values as  x_1 and  y_1 or  x_2 and  y_2 .

On a side note, it would be best if you could at least attempt the question. TeeEm does not take kindly to people just asking for answers
Nope i cant do it:/ give me the starting line?
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Louisb19
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(Original post by Ayaz789)
Nope i cant do it:/ give me the starting line?
Could you link me to the question paper or screenshot the question please.
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