Parametric equations

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 Qaq²,2aq)
find the gradient of the chord
then let q tend to p, ie set q=p

I still dont understand it sorry :/

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 retarded

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

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?

of course with it!

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

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

$\dfrac{\mathrm{d}y}{\mathrm{d}x} (x_1 - x_2) = y_1 - y_2$

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?