Question

The locus of the middle 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

Answer 1

`4x-5y=20`
`4x_1-5y_1=20`
`4x_1-20=5y_1`
`y_1=4/5x_1-4`
`x x_1+yy_1=9`
`hx+ky=h^2+k^2`
`x_1/h+y_1/k=9/h^2`
`x/h=(4/5x_1-4)/(k)=9/(h^2+k^2)`
`kx_1=4/5x_1h-4h`
`4x_1h-5kx_1=20h`
`x_1(4h-5k)=20h`
`x_1=(20h)/(4h-5k)`
`x_1/h=9/(h^2+k^2)`
`h/x_1=(h^2+k^2)/9`
`(4h-5k)=20(h^2+k^2)`
`20(h^2+k^2)-9(4h-5k)`
`20(x^2+y^2)-36x+45y=0`
option A is correct.