If A=(2,3) and B=(-4,5) are two fixed points, then the locus of a point P such that the area of P A B is 12 square units is

Step-by-step solution

Let the co-ordinate of the point P is (x₁, y₁ ) . Then, the area of the triangle =12 1 2 | array ccc 2 & 3 & 1 -4 & 5 & 1 x₁ & y₁ & 1 array |=12 aligned & |2 (5-y₁ )-3 (-4-x₁ )+1 (-4 y₁-5 x₁ ) |=24 & |10-2 y₁+12+3 x₁-4 y₁-5 x₁ |=24 & |-2 x₁-6 y₁+22 |=24 & 2 x₁+6 y₁-22= 24 & x₁+3 y₁-11= 12 & (x₁+3 y₁-23 )=0 or (x₁+3 y₁+1 )=0 aligned Hence, the locus is :- aligned & (x+3 y-23)(x+3 y+1)=0 & x^2+6 x y+9 y^2-22 x-66 y-23=0 aligned