Suppose a point P moves so that BP ^2- AP ^2=121 , where A and B are (2,5) and (5,11) respectively. Then the locus of P is a straight line, whose slope is

Step-by-step solution

Let P (h, k) be the point B P^2-A P^2=121 aligned & (11-k)^2+(5-h)^2-(h-2)^2-(k-5)^2=121 & 121+k^2-22 k+25+h^2-10 h-h^2-4+4 h & -k^2-25+10 k=121 aligned aligned & -6 h-12 k=4 & h+2 k=-4 / 6 & 2 k=-h-4 / 6 & k=-1 / 2 h-4 / 12 & y=-1 / 2 x-1 / 3 & m=-1 / 2 aligned