A line through `A(-5,-4)` meets the lines `x+3y+2=0,2x+y+4=0a n dx-y-5=0` at the points `B , Ca n dD` rspectively, if `((15)/(A B))^2+((10)/(A C))^2=(6/(A D))^2` find the equation of the line.

Explanation

Let `theta` be the inclination of line through `A(-5,-4)`


Therefore, equation of this line is
`(x-x_1)/(costheta)=(y-y_1)/(sintheta)=r`
`(x+5)/(costheta)=(y+4)/(sintheta)=r_1 `

So,
`x=(rcostheta-5)` and `y=(rsintheta-4)`
So,
Coordinates of A are
`(−5+rcostheta,−4+rsintheta)`

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