The equation of the chord of the circle `x^2+y^2-3x-4y-4=0` , which passes through the origin such that the origin divides it in the ratio 4:1, is `x=0` (b) `24 x+7y=0` `7x+24=0` (d) `7x-24 y=0`

Options

A. `x=0`
B. `24x+7y=0`
C. `7x+24y=0`
D. `7x-24y=0`

Answer

2

Explanation

Let `y=mx` be a chord.
Then the points of intersections are given by
`x^(2)(1+m^(2))-x(3+4m)-4=0`
`:. x_(1)+x_(2)=(3+4m)/(1+m^(2))` and `x_(1)x_(2)=(-4)/(1+m^(2))`
Since `(0,0)` divides chord in the ratio `1:4`, we have
`x_(2)= -4x_(1)`
`:. -3x_(1)=(3+4m)/(1+m^(2))` and `4x_(1)^(2)=(-4)/(1+m^(2))`
`:. 9+9m^(2)=9=9+16m^(2)+24m`
i.e., `m=0,-(24)/(7)`
Therefore, the lines are `y=0` and `y+24x=0`