Fitzpatrick 3u Question Parametrics (1 Viewer)

[silentk99]

Im stuck on this question for 4 hours. Its from Fitzpatrick 3u ex 24c, q 24. Any help appreciated.

P(2at,at^2) and q(2as,as^2) are two points on the parabola x^2=4ay. The chord pq subtends an right angle at origin O. If r is the fourth vertex of the rectangle poqr, show that:

1)ST=-4 (i GOT THIS PART)

2) Show that R is represented parametrically by x = 2a(t^2-4)/t, y=a(t^4+16)/t^2 (Need help with this part.)

 

[leehuan]

This is the wrong thread to be posting this >_>

Also, what is T?

 

[b0b101]

Im stuck on this question for 4 hours. Its from Fitzpatrick 3u ex 24c, q 24. Any help appreciated.

P(2ap,ap^2) and q(2as,as^2) are two points on the parabola x^2=4ay. The chord pq subtends an right angle at origin O. If r is the fourth vertex of the rectangle poqr, show that:

1)ST=-4 (i GOT THIS PART)

2) Show that R is represented parametrically by x = 2a(t^2-4)/t, y=a(t^4+16)/t^2 (Need help with this part.)

Made it nice and neat for you...

 

[silentk99]

Made it nice and neat for you...

Thanks,

Its not p but t

 

[InteGrand]

Im stuck on this question for 4 hours. Its from Fitzpatrick 3u ex 24c, q 24. Any help appreciated.

P(2at,at^2) and q(2as,as^2) are two points on the parabola x^2=4ay. The chord pq subtends an right angle at origin O. If r is the fourth vertex of the rectangle poqr, show that:

1)ST=-4 (i GOT THIS PART)

2) Show that R is represented parametrically by x = 2a(t^2-4)/t, y=a(t^4+16)/t^2 (Need help with this part.)

 

[silentk99]

I tried that but the algebra was not working

 

[Ambility]

I tried that but the algebra was not working

Here's the full algebra working for you then. This is done using the method Integrand suggested, finding the equations for QR and PR, and then finding R by simultaneously solving these equations.