1.

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 `x^2+y^2=9` is : (A) `20(x^2+y^2)-36+45y=0` (B) `20(x^2+y^2)+36-45y=0` (C) `20(x^2+y^2)-20x+45y=0` (D) `20(x^2+y^2)+20x-45y=0`

Answer» `ax+((4a-20)/5)y=9-(1)`
Let P(h,k) is midpoint of chord of contract
`hx+ky=h^2+k^2-(2)`
`5ax+(4a-20)y=45-(3)`
Comparing equation 2 and 3
`h/(5a)=k/(4a-20)=(h^2+k^2)/45`
`h/(5a)=k/(4a-20)`
`h(4a)-20h=52k`
`a=(20h)/(4h-5k)`
`h/(5a)=(h^2+k^2)/45`
`h(4h-5k)/(100h)=(h^2+k^2)/45`
`36h-45k=20(h^2+k^2)`
`20(x^2+y^2)=36x-45y`
`20(x^2+y^2)-36x+45y=0`.


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