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Let the general equation of a line (L1) be of the form x/a+y/b=1 Let (h,k) lie on this line such that a normal line(L2) passing through this point intersects at the origin. Now we know that L1 is perpendicular to L2. Thus we get,
(k/h)*(-b/a)=-1
Which implies that:
k/h=a/b
Also, we know from the information provided in the question that ab=a^2+b^2, 1=a/b+b/a
From the manipulation we did above we get,
1=k/h+h/k which implies that
h^2+k^2=hk or x^2+y^2=xy.
Regards
Arun (askIITians forum expert)
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