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Thanks vds700 for clearing that up. :)

Thanks, we're off to a good start. :)

I've got a whole pile of questions I need help with, but I have restricted access to the internet at the moment, so I mightn't be able to check back here for a little while. Lets hope you guys can help me out. If a the displacement of a particle moving in simple harmonic motion is given by x =...

Got another one; Twenty-five wallabies are released on Wombat Island and the population is observed over the next six years. It is found that the rate of increase in the wallaby population is given by dP/dt = 12t - 3t2, and the population itself is given by P = 25 + 6t2 - t3. When does the...

Ooooh... I don't know why I didn't make the jump from diameter to radius. Thanks. :)

I'm not quite sure how to approach this question, could someone help me out here? It asks; A certaing brand of medicine tablet is in the shape of a sphere with diameter 5mm. Ther rate at which the pill dissolves is dr/dt = -k, where r is the radius of the sphere at time t hours, and k is a...

Hmm... I followed a similar process when trying to figure out c), but couldn't get the correct answer. According to the sheet, the locus of T should be y = -a (i.e. the directrix). While I'm here I may as well post the the answers to d) as well. N should be [-apq(p + q), a(p2 + pq + q2 + 2)]...

I'd like to double check my working for this question to make sure I have it right; a) Write down the equation of the chord joining the points P (2ap, ap2) and q (2aq, aq2) on the parabola x2 = 4ay. [I think I've got this working down. I'm not sure if it should plus apq or minus apq in the...

Thanks. Now time for another; How can I solve the two equations x + py = p3 + 2p and x + qy = q3 + 2q simultaneously to find the point of intersection (-pq(p + q), p2 + q2 + pq + 2)? EDIT: Never mind, got it. Thanks again Tommy. :)

Ignore the last question, I've got a new one. Again, I'm having problems visualising exactly what the question asks. Here it is; PQ, a variable chord of the parabola x2 = 4y, subtends a right angle at the vertex O. a) If p and q are parameters corresponding to P and Q, show that pq = -4. b)...

Tommy saved me again with the last question, but now I have another; The tangent at T (4t, 2t2) on the parabola x2 = 8y has equation y - tx + 2t2 = 0. a) This tangent meets the parabola x2 + 4y = 0 in P and Q. Show that the abscissae x1 and x2 of the points P and Q are the roots of the...

I'm having problems with another question, largely because I'm having a bit of trouble visualising what the question asks. Here's the question; The equation of the tangent at a variable point T (2t, t2) on x2 = 4y is y - tx + t2 = 0. This tangent meets the tangent at the vertex O in R and the...

Ooooooooh... I get it now. I have no idea why I didn't see that earlier. Thanks very much.

How do you establish that the locus is (0, 1)? Is it just an assumption?

Thanks for all your help Tommy. Now, time for another question; P (2p, p2) is a variable point on the parabola x2 = 4y, whose focus is S and vertex O. M and N are the midpoints of SP and OM respectively. a) Show the locus of M is the parabola y = 1/2(x2 + 1) and find the locus of N. I'm...

Sorry, got halfway through typing it up and accidentally deleted it. I'll type up the full question... The equation of the tangent at P(2ap, ap2) on the parabola x2 = 4ay (whose vertex is 0) is y - px + ap2 = 0. The tangent meets the x-axis at Z (ap, 0) and the y-axis at T (0, -ap2). PN is...

I'm having trouble with part iv and v of the same question. Can I see your answers?

For Z (I'm assuming you mean the first question); = (0) - px - ap2 = px = ap2 = x = ap therefore Z = (ap, 0)

I'm having trouble with a particular parametric parabola question. Can someone go through them with me so I can understand? Here it is; Prove that SP = a(p2 + 1) units [where S = (0, a) or the focus, and P = (2ap, ap2)] and hence that SZ2 = OS x SP [where O is the origin].

So... I've been having a fair bit of trouble with this particular exercise I'm working on at the moment, so be prepared for a rush of questions. You ready? Okay, here we go; 1. a) Find the area enclosed between the curve y = 1/√(1 - x2), the x-axis and the lines x = 0 and x = 1/2. (This part...