The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x−5y=20 to the circle x2+y2=9 is
Here, equation of chord of contact w.r.t P is
xλ+y(4λ−205)=9
5λx+(4λ−20)y=45……(i)
And equation of chord bisected at the point Q (h, k) is
xh+yk−9=h2+k2−9⇒xh+ky=h2+k2……(ii)
From Eqs. (i) and (ii), we get
5λh=4λ−20k=45h2+k2∴ λ=20h4h−5k and λ=9hh2+k2⇒20h4h−5k=9hh2+k2or 20(h2+k2)=9(4h−5k)or 20(x2+y2)=36x−45y