A triangle PQR is inscribed in the parabola x2=8y such that ∠Q=π2 . Let L1,L2be the tangents drawn at P, R respectively. If the equation of the parabola whose axis is along y-axis, whose latus rectum is along x-axis and its length is the minimum length of intercept on x-axis cut off by L1,L2  is   y=ax2+bx+c,then, which of the following is/are true?

P=4t1,2t12,Q=4t2,2t22,R=4t3,2t32PQ⊥QR=t1+t2t2+t3=−4⇒t22+t1+t3t2+t1t3+4=0Δ≥0⇒t1+t32-4t1t2+4≥0⇒t1−t3≥4 Minimum length of intercept by L1,L2 on x-axis =2t1−t3=8given parabola is y=ax2+bx+c , whose axis is y-axis ,so b=0and length of the latusrectum is =1a= mininmum of L1L2=8⇒a=±18 and the parabola passing through the points 4,0 and -4,0⇒c=±2 Parabola is y=x28−2( or )y=−x28+2