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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?



Your Answer
A

ax = by 

Your Answer
B

ax2 = by

Correct Answer
C

ay = bx

Your Answer
D

ay2 = bx


Solution

The correct option is C

ay = bx


Let 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(ba))2=(x(ab))2+(y(a+b))2
Squaring both sides,
(x(a+b))2+(y(ba))2=(x(ab))2+(y(a+b))2(x(a+b))2(x(ab))2=(y(a+b))2(y(ba))2
We can use this identity a2b2=(a+b)(ab) to solve the above equation. After solving, we will get:
ay = bx

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