Let \(T\) be the tangent to the parabola \({y}^{2}=16x\) at the point \((64, 32)\). Let \(L\) be the tangent to the same…

Let \(T\) be the tangent to the parabola \({y}^{2}=16x\) at the point \((64, 32)\). Let \(L\) be the tangent to the same parabola at another point (\({x}_{1},{y}_{1}\)) on the parabola. If \(L\) and \(T\) are perpendicular to each other, then the distance between the point \(\left({x}_{1},{y}_{1}\right)\) and the focus of the parabola, is

[JEE Advanced 2026]