If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), then which of the following is correct
bx = ay
Let, P(x,y), Q(a + b, b - a) and R(a - b, a + b) are the given points.
Then, according to question:
PQ = PR (Given)
⇒√{x−(a+b)}2+{y−(b−a)}2=√{x−(a−b)}2+{y−(a+b)}2
Squaring both sides,
⇒{x−(a+b)}2+{y−(b−a)}2={x−(a−b)}2+{y−(a+b)}2
⇒x2−2x(a+b)+(a+b)2+y2−2y(b−a)+(b−a)2
=x2+(a−b)2−2x(a−b)+y2−2y(a+b)+(a+b)2
⇒−2x(a+b)−2y(b−a)=−2x(a−b)−2y(a+b)
⇒ax+bx+by−ay=ax−bx+ay+by
⇒2bx=2ay⇒bx=ay