The line $y=6 x+1$ touches the parabola $y^2=24 x$. The coordinates of a point $P$ on this line, from which the tangent to $y^2=24 x$ is perpendicular to the line $y=6 x+1$, is

Given, equation of line is y = 6x + 1 and equation of pa rab ola is $y^2=24 x$. The locus of the point of intersection of perpendicular tangent to a parabola is its directrix. So, required point is the point of intersection of y = 6x + 1 and direc trix x = − 6. Hence, its coordinates are (− 6, − 35).