Parameters (1 Viewer)

[steve001]

Hey,

Just another questiopn on parameters:
P(2at,at^2) is a variable point on the parabola x^2 = 4ay, whose focus is S. Q (x,y) divides the interval from P to S in the ratio t^2:1
(i) Find x and y in terms of a and t. (i got Q(2at/t^2+1,2at^2/t^2+1))
(ii) Verify that y/x = t
(iii) Prove that, as P moves on the parabola, Q moves on a circle, and state its centre and radius. (this is the bit i cant do)

 

[scardizzle]

part (ii) would be useful

Also just to confirm for part (i) did you get Q as ( 2at/(t^2 +1), 2at^2/(t^2+1)) ?

 

[steve001]

yer thats what i got for Q

 

[scardizzle]

hence Q is a circle with centre (0,0) and radius (2ay)^1/2

hope that's right...

 

[steve001]

thanks for the help and it looks right to me

 

[random-1005]

hence Q is a circle with centre (0,0) and radius (2ay)^1/2

hope that's right...

t is meant to be replaced with (y/x) not (x/y) in the second line

 

[untouchablecuz]

hence Q is a circle with centre (0,0) and radius (2ay)^1/2

hope that's right...

the radius isn't (2ay)^1/2 or else the locus woudn't be a cirle (variable radius)

after completing the square you get: x^2 + (y-a)^2 = a^2

the correct locus is a circle with centre (0,a) and radius a

 

[scardizzle]

yeah sorry my bad, i made a bit of a mess on that question