If the line `l x+m y+n=0` touches the circle `x^2+y^2=a^2` , then prove that `(l^2+m^2)^2=n^2dot`

Explanation

If the line lx+my+n=0 touches the circle `x^2+y^2=a^2`, then length of the perpendicular from its centre O(0,0) is equal to its radius a.


Therefore,
`(​l×0+m×0+n)/(sqrt(l^2+m^2))=a`


`(l^2+m^2)a^2=n^2`, which is the required condition.