I think I'm making a mistake. (LOCUS) (1 Viewer)

[Accelerando]

J&C Book 2 Exercise 23.2 Q1 a) :
Find the equation of the chord joining:
t1 = 2, t2 = -1 on
x=2t,
y=t^2.
Show that this chord passes through the focus.

I got to the equation of the chord (x-2y+4=0), but the focus part!

from the set of parametric equations,
t= x/2.

substituting t into y=t^2 :
y=(x/2)^2
x^2=4y

since a parabola is in the form x^2=4ay, a=1.
hence the focus is (0,1).

But this coordinate does not satisfy the equation of the chord?!?!

What am i doing wrong?

 

[blackops23]

Strange... works for part(b) though, maybe it's a mistake?

EDIT: yeah it's gotta be a mistake, because the parameters of a focal chord are t and -1/t, which doesn't apply to 2 and -1. Look at part(b), parameters are 2 and -0.5, which do satisfy the focal chord's parameters: t and -1/t

 

[Bored Of Fail 3]

all looks correct, mostly likely the answer in the back of the book is wrong

 

[Accelerando]

In other words, that chord is not the focal chord?

Thank you guys!