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Two points P(2ap, ap^2) and Q(2aq, q^2) lie on the parabola x^2 = 4ay. i. Show that the equation of the tangent to the parabola at P is y = px - ap^2. ii. The tangent at P and the line through Q parallel to the y axis intersect at T. Find the coordinawtes of T. iii. Write down the...

Thanks alakazimmy, that's brilliant. I'm finally starting to understand these questions - slowly but surely. I do have a couple more, but I think I might work on them a bit longer before posting them here. Thanks for all your help so far, much appreciated.

Yeah, the 'axis' is a bit ambiguous, but that's all the question says. Okay, thanks a lot for that alakazimmy. That's really helped. I've moved onto some of the tougher questions now. And I have another one i need help with. It involves solving simultaneous equations mostly, but its...

P is a variable point (2t, t^2) on the parabola x^2=4y, whose vertex is O. M, N, are the feet of the perpendiculars from P on to the axis and directrix respectively. R is the midpoint of OP and L is the midpoint of MN. Find the locus of: i) R ii) L ...why must parametrics be so hard... :'(

...burettes AND pipettes are used in titration instead of just one or the other? Cause from what I know they perform pretty much the same function...

5.267 anhydrous sodium carbonate was dissolved in water in a volumetric flask and the volume made up to 250 mL. 10 mL of this solution was pipetted into a concial flask, and titrated with hydrochloric acid. 21.3 mL was needed to reach the equivalence point. Calculate the molarity of the...

lolokay, could you please explain to me how you got from here: 7^(n+1) + 3(n+1)7^(n+1) - 1 is divisble by 9 to here?: 7 x 7^n + 7 x 3n x 7^n - 7 + 3 x 7^(n+1) + 6 In particular, i can't quite see where you got the bolded parts from... I know it has to eventually equal 1, as in the...

Prove by mathematical induction that 12/(1x3x4) + 18/(2x4x5) + 24/(3x5x6) + ... + [6(n+1)]/[n(n+2)(n+3)] = 17/6 - 1/(n+1) - 1/(n+2) - 4/(n+3) I'm seriously so bad at these.

Ah okay brilliant. Thanks. We hadn't learned that cava/a = cbvb/b formula yet, so I'm not quite sure what the stoichiometric coefficient is at the moment. But thanks anyway. Does this formula apply to all the questions? Could you possibly type out the working for me? I'm having a little...

In a titration, 25.0 mL of sodium hydroxide solution was pipetted into a conical flask. A 0.100 mol/L solution of sulfuric acid was run from the burette into the flask. An indicator in the flask changed colour when 22.0 mL of the acid had been added. a) Write a balanced equation for the H...

What does 2cos^3(x) have to do with anything when the question involves cos^2 3x? I'm not being mean here, even though it sounds it. I really do appreciate your help.

Sorry, this'll seem idiotic, but how did you work out the bolded line?

int. from pi/4 to 0 of cos^2 3x What do you do here? My solutions look totally odd. Is it a product rule? Would it be easier to use a chain rule or something? Thanks.

Dont know where the formula is in my textbook. I dont recall ever being told how one might apply it to such a situation... The velocity of a projectile 2seconds after its launch can be found from the vector diagram (on the right). What was the launch velocity of the projectile? Here's the...

3 x 600 x 800 x 30 x 3 x 16 = 2073600000 BITS ^So, is there an extra 3 in there? (seconds) x (resolution) x (FPS) x (bit depth)

Like, how to do video size, image size and sound file size? Thanks :)

Not 100% on this one, but I'm thinking that if the Expert System couldn't come to a conclusion as to what it was, it wouldn't be within its records. I say this because there is no "fuzzy logic" in an expert system, only neural networks (where inference engines are not used). Therefore...

Vertex you can work out as (h, k) I believe. If you know the vertex first, then you can figure out focus and directrix easily by moving "a" units along a number plane/graph/whatever they're called.

Also, it might help to know... It doesn't affect the value of it, since you are essentially multiplying by 1 to get it to be rational. (root6/root6 = 1)

For the second question... The two charges repel, so there will be field lines going AWAY from the two charges and nothing inbetween them (since diagrams show the flow of negative particles in a field). The null point will be in the middle of the two points, but since one is 2x as strong as...