Let S denote the locus of the point of intersection of the pair of lines 4 x-3 y=12 4 x+3 y=12 where varies over the set of non-zero real numbers. Let T be the tangent to S passing through the points (p, 0) and (0, q), q>0, and parallel to the line 4 x- 3 2 y=0. Then the value of p q is
A. -6 2
. array l 4 x-3 y=12 \\ 4 x+3 y= 12 array \ 16 x^2-9 y^2=144 aligned & x^2 9 - y^2 16 =1 Curve :S \\ & T: y=m x 9 m^2-16 \\ & m= 4 2 3 \\ & y= 4 2 x 3 32-16 \\ & 3 y=4 2 x 12 \\ & as q>0 \\ & 3 y=4 2 x+12 \\ & p=- 3 2 \& q=4 \\ & p q=-6 2 aligned
Related: Mathematics — Pair of Lines · All PYQ Banks