As `L_(1)andL_(2)` are normals to `x^(2)+y^(2)=72`, they must be of the form y=mx.
Sloving it with parabola `4x^(2)-4x-24y+49=0`, we have
`4x^(2)-4x-24mx+49=0`
`or4x^(2)-4x(1+6m)+49=0`
Since the lines touch the parabola,
D=0
`or16(6m+1)^(2)-16xx49=0`...