A parabola whose focus is  $S(6,8)$ is touching the co-ordinate axes, then which of the following statement(s) is/are correct?

The equation of circle whose diameter is the portion of the tangent at the vertex of the parabola between the co-ordinate axis is  $x^2+y^2-6x-8y=0$

If P and Q are the ends of a focal chord of the parabola, then $\frac{1}{SP}+\frac{1}{SQ}=\frac{5}{24}$

If P and Q are the ends of a focal chord of the parabola, then $\frac{1}{SP}+\frac{1}{SQ}=\frac{1}{5}$

Equation of the latus rectum is $4x+3y=48$