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), q0 , and parallel to

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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

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Correct answer: 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

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

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