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Question

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x5y=20 to the circle x2+y2=9 is

A
20(x2+y2)36x+45y=0
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B
20(x2+y2)+36x45y=0
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C
36(x2+y2)20y+45y=0
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D
36(x2+y2)+20x5y=0
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Solution

The correct option is A 20(x2+y2)36x+45y=0

Here, equation of chord of contact w.r.t P is
xλ+y(4λ205)=9
5λx+(4λ20)y=45(i)


And equation of chord bisected at the point Q (h, k) is
xh+yk9=h2+k29xh+ky=h2+k2(ii)
From Eqs. (i) and (ii), we get
5λh=4λ20k=45h2+k2 λ=20h4h5k and λ=9hh2+k220h4h5k=9hh2+k2or 20(h2+k2)=9(4h5k)or 20(x2+y2)=36x45y






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