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????
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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????
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
Means find f if p=f(q) or g if q=g(p)Quote:
Originally Posted by vixity
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".Quote:
Originally Posted by vixity
It is actually looking for it in the form pq = -1. I've seen this question before and the exam board mark scheme.Quote:
Originally Posted by krtxmrtz
So the relationship is in other words the equation of chord pq which is -1, btw are you from Australia?
Its derived from the equation of the chord but isn't the equation of the chord.
I'm from England