Can You Solve This ?

Geometry Level 4

A circle is drawn whose centre is the focus of the parabola \({ y }^{ 2 }=16x\). Both the ends of latus rectum of the parabola are points on the circle. At the end of latus rectum in the 4th quadrant, a tangent is drawn to the parabola which intersect the circle at a point B on the x-axis. A triangle is formed having its vertices as the end points of latus rectum and the point B. The area of this triangle is a root of the cubic equation \({ x }^{ 3 }-69{ x }^{ 2 }+326x-384=0\). The other two roots of this cubic equation are 'a' and 'b'.

If \(g(x)={ x }^{ 2 }-5x+4\) then \(g(x)+b=0\) also have the roots a and b, then find the which of the following points lie on the curve \(xy = a/b\) :

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