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![[Post New]](/templates/default/images/icon_minipost_new.gif) 2 Dec 2007 12:41:50 IST
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if P,Q,R be three co-normal pts. of y2=4ax whose normals pass through T,then SP.SQ.SR= a.ST2
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there are numerous options besides I.I.T
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let P Q , R be points t1,t2, t3, T be (h,k)
eqn of normal
y+tx=2at+at^3
it passes thru (h,k)
so at^3 + (2a-h)t - k=0 (i)
SP=dist of P frm focus=dist of P frm directrix (x+a=0)
SP=a(t1^2+1)
similarly SQ=a(t2^2+1), SR=a(t3^2+1)
SP.SQ.SR = a^3((t1t2t3)^2 + (sigma) (t1t2)^2 + (sigma)(t1)^2 + 1
u can find d values of t1t2t3, sigma (t1t2)^2 and sigma(t1)^2 frm eqn (i)
put them n u'll get the answer
nudge me if any doubt
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