November 30th, 2009, 05:18 AM  #1 
Senior Member Joined: Sep 2008 Posts: 199 Thanks: 0  coordinate geometry
Two variable points P(ap^2,2ap) and Q(aq^2,2aq) on the parabola y^2=4ax are such that PQ subtends a right angle at the origin. (1) Show that the chord PQ passes through a fixed point on the xaxis. Gradient of PQ = 2/(p+q) Equation of PQ: , when y=0, I found x=apq, which means the chord PQ cuts the xaxis at (apq,0) Am I correct? (2) Find the locus of the point of intersection of the tangents to the parabola at P and Q . I found the point of intersection of the tangents to be (apq , a(p+q)) and here I am not sure how to move on. THanks for helping. 
November 30th, 2009, 11:41 PM  #2  
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: coordinate geometry Quote:
 
December 1st, 2009, 08:52 AM  #3  
Global Moderator Joined: Dec 2006 Posts: 20,370 Thanks: 2007  Quote:
Quote:
 
December 1st, 2009, 09:45 PM  #4  
Senior Member Joined: Sep 2008 Posts: 199 Thanks: 0  Re: Quote:
so x=apq , y=a(p+q) and the locus here would be x=4a I understood all this but I don't understand what u mean by 'You can show the ycoordinate can have any value'  
December 2nd, 2009, 12:58 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,370 Thanks: 2007 
Please don't quote the entire post you are replying to if your reply would make just as good sense without your doing so, which is usually the case when replying to the immediate preceding post. If you want a(p + q) to have the value r, p and q must be the roots of t²  (r/a)t  4 = 0. Whatever real value r has, that equation has real roots. 

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