On the locus of the point P(x, y) equidistant from (3,0) and (0,4) . If A and B are two points that satisfy 4 x=3 y and x=y respectively, then the distance between A and B is

Step-by-step solution

P Q=P R aligned & (x-3)^2+(y-0)^2 = (x-0)^2+(y-4)^2 & x^2-6 x+9+y^2=x^2+y^2-8 y+16 & 6 x-8 y+7=0 & y= 6 x+7 8 aligned Let A= ( , 6 +7 8 ) and B= ( , 6 +7 8 ) According to question, 4 =3 ( 6 +7 8 ) and = 6 +7 8 = 3 2 and = 7 2 aligned & A= ( 3 2 , 2 ) and B= ( 7 2 , 7 2 ) & A B= ( 3 2 - 7 2 )^2+ (2- 7 2 )^2 = 5 2 aligned