whatever be the value of `theta`, the line `y = (x-11) cos theta - cos 3 theta` is always normal to the parabola

Explanation

The slope of the given line is m `=costheta`.
Also, normal to parabola `y^(2)=16x` having slope m is
`y=mx-8m-4m^(3)`
`:." "y=xcostheta-8costheta-4cos^(3)theta`
`:." "y=xcostheta-11costheta+3costheta-4cos^(3)theta`
`:." "y=(x-11)costheta-cos3theta`
so, this line is always normal to parabola `y^(2)=16x`.