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Solving problems in co-ordinate geometry with given set of conditions causes difficulties at times One such case is equation of family of lines. The equation y -1 = m (x -2) represent a family of lines passing through (2,1). But this does not include the line x -2 =0. Since the slope of the line x -2 =0 is infinity. Therefore in case there are two solutions to a problem and only one solution is being obtained aigebralcally we have to re-examine. A line y = mx through origin cuts the parallel lines x + y =3 and y =5at A and B respectively. The distance between the two points of intersection is d. If AB=2 then the quadratic equation formed is |
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Answer» `(4-d^(2)) m ^(2) + 2md ^(2) + 4-d ^(2) =0` |
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