Subject: Parabola and its focus
Date: Tue, 22 Jul 1997 14:42:34 +0800
From: Calvin Lui
Hi I am Ronald.
I have a mathematics question that I can't solve it.
The question is :
P(2t,2(t^2)) is a point on the parabola y= (x^2) /2 .Q and R are two points on the parabola such at PQ passes through the focus and PR is perpendicular to the axis of the parabola.Find the coordinates of Q and R.
I can find the coordinate of R but can't find the coordinate of Q!
I have tried to solve it.I found that the equation of PQ must be : (4t^2-1)x -4ty+2t=0.Then I let (2u,2u^2)be the coordinate of Q and put it into the equation.!
so ,i found that u =8t^2+1/ 8t or u=-1/8t... However ,the real answer(ie,the coordinate of Q )is(-1/2t,1 /8(t^2)) Could you please help me to solve the problem?