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Analytical Geometry
5 Feb 2012 18:08:10 IST
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6 Feb 2012 18:34:28 IST
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Ohh..I'm sorry i got confused between another property...
Yeah the answer is (4a,0)...
As a penalty for wrong answer, I'll write the solution here....
Let co-ordinates of A and B be (at12,2at1) and (at22,2at2). [t1 and t2 are parameters]
They lie on the parabola, evidently.
Slope of OA=2/t1
Slope of OB=2/t2
Therefore, (2/t1)*(2/t2)=(-1)
or, t1t2=(-4)
Now equation of line joining AB is
(t1+t2)y=2(x+at1t2) (You can derive it..)
Putting t1t2=-4,
(t1+t2)y=2(x-4a)
Therefore it always is satisfied by (4a,0).
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It will pass through the focus (a,0).
It is a property of the parabola.