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

Q: 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

. 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

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. 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

Pair of Lines — Previous Year Questions & Solutions