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![[Post New]](/templates/default/images/icon_minipost_new.gif) 29 Nov 2007 10:41:43 IST
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x^2-4y^2=4 (A conic)
x^2+4y^2=4 (B conic)
frm point (x1, y1) of A, tangents r drawn to B
so eqn of chord of contact will be
xx1+4yy1=4 (i)
let mid point of Q, R be (h, k)
eqn of a chord whose mid point is (h, k) is
T=S1 or hx+4ky-4=h^2+4k^2-4
or hx+4ky=h^2+4k^2 (ii)
compare eqns (i) and (ii), u'll get]
x1/h = y1/k = 4/(h^2+4k^2)
so u get values of x1 n y1 in terms of h, k
this x1, y1 lies on conic A, so satisfy the value of x1, y1 u got in conic A, u'll get the locus of mid-point
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