Given equation of line x−y=0 Distance from P(α,β) to line x−y=0 is b=|
α−β
√2
|⇒(α−β)2=2b2 . . . (i) Distance between P(α,β) and A(2,1) is a2=(α−2)2+(β−1)2 . . . (ii) Distance from origin to A(2.1) is C2=5 Alsoa=bc ∴a2=5b2 . . . (iii) From Eqs. (i), (ii) and (iii), we get (α−2)2+(β−1)2=
5(α−β)2
2
2(α2−4α+4+β2−2β+1]=5[α2+β2−2αβ] ⇒3(α2+β2)−10αβ+8α+4β−10=0 ∴ Locus of P is 3(x2+y2)−10xy+8x+4y−10=0