Err locus and parabola?

[vixity]

The points P(2ap, ap^2) and Q(2aq, aq^2) lie on the parabola x^2=4ay. The chord PQ passes through the point (0,a) find the relationship between p and q.

What the hell is the relationship????

[Glaysher]

Gradient of chord = (aq² - ap²)/(2aq - 2ap)

= (q² - p²)/[2(q - p)] = [(q + p)(q - p)]/[2(q - p)]

= (q + p)/2

Equation of chord = y - ap² = [(q + p)/2](x - 2ap)

x = 0 y = a

a - ap² = [(q + p)/2](-2ap)

a(1 - p²) = [(-2ap)(q + p)/2]

1 - p² = -p(q + p)

1 - p² = -pq - p²

1 = -pq

pq = -1

[krtxmrtz]

What the hell is the relationship????

Means find f if p=f(q) or g if q=g(p)

[vixity]

woah **** you people are smart..tell me how old are you people and where are you from?

[krtxmrtz]

woah **** you people are smart..tell me how old are you people and where are you from?

Click on the poster's name and select "View Public Profile".

[Glaysher]

Means find f if p=f(q) or g if q=g(p)

It is actually looking for it in the form pq = -1. I've seen this question before and the exam board mark scheme.

[vixity]

So the relationship is in other words the equation of chord pq which is -1, btw are you from Australia?

[Glaysher]

Its derived from the equation of the chord but isn't the equation of the chord.

I'm from England