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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


A

by = ax

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B

bx = ay

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C

bx = a

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D

x = ay

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Solution

The correct option is B

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(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

x22x(a+b)+(a+b)2+y22y(ba)+(ba)2

=x2+(ab)22x(ab)+y22y(a+b)+(a+b)2

2x(a+b)2y(ba)=2x(ab)2y(a+b)

ax+bx+byay=axbx+ay+by

2bx=2aybx=ay


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