Pls solve this question and explain me clearly what is locus
If the equation of the lous of a point equidistant from the points (a1, b1) and (a2,b2) is (a1-a2)x+ (b1-b2)y+c=0 then find the value of c.
Let (x,y) be equidistant from (a1, b1) and (a2,b2)
Then using distance formula
(a1 - x)2 + (b1 - y)2 = (a2 - x)2 + (b2 - y)2
Open the squares the solve
a12 + x2 - 2 a1 x + b12 + y2 - 2 b1 y = a22 + x2 - 2 a2 x + b22 + y2 - 2 b2 y
a12 - 2 a1 x + b12 - 2 b1 y = a22 - 2 a2 x + b22 - 2 b2 y
2(a1 - a2) x + 2(b1 - b2)y + [a22 + b22 - a12 - b12 ] = 0
Divide the whole equation by 2
On comparing with (a1-a2)x+ (b1-b2)y+c=0
c = [a22 + b22 - a12 - b12 ] /2