Question

# 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?

A

ax = by

B

ax2 = by

C

ay = bx

D

ay2 = bx

Solution

## The correct option is C ay = bxLet points A(a + b, a - b) and B(a - b, a + b) be equidistant from point P (x, y ). By, distance formula PA = PB,  √(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⇒(x−(a+b))2−(x−(a−b))2=(y−(a+b))2−(y−(b−a))2 We can use this identity a2−b2=(a+b)(a−b) to solve the above equation. After solving, we will get: ay = bx

Suggest corrections