For two points A(2,1) and B(1,2), P is a point such that P A: P B=2: 1 , then locus of P is

Step-by-step solution

Two points A(2,1) and B(1,2) and another point P , is such that P A: P B=2: 1 . Let us assume P is (x, y) Now, using distance formula and aligned & P A= (x-2)^2+(y-1)^2 & P(B)= (x-1)^2+(y-2)^2 & P A P B = 2 1 = (x-2)^2+(y-1)^2 (x-1)^2+(y-2)^2 = 2 1 aligned Squaring both sides aligned & (x-2)^2+(y-1)^2 (x-1)^2+(y-2)^2 = 4 1 & x^2-4 x+4+y^2-2 y+1 & =4 (x^2-2 x+1+y^2-4 y+4 ) & x^2-4 x+4+y^2-2 y+1 & =4 x^2-8 x+4+4 y^2-16 y+16 & 3 x^2+3 y^2-4 x-14 y+15=0 aligned