If the point R(x, y) is equidistant from the points P (a+ b, a-b) and Q (b- a, a+b), then find distance of P from origin, mid-point of PQ and also prove that xa = yb

please explain

Sneha

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Saturday, 28 November 2020 08:31 AM

$?+=+$

$?{x-(a+b)}_{2}+{y-(b-a)}_{2}={x-(a-b)}_{2}+{y-(a+b)}_{2}$

$?x_{2}-2x(a+b)+(a+b)_{2}+y_{2}-2y(b-a)+(b-a)_{2}$

$=x_{2}+(a-b)_{2}-2x(a-b)+y_{2}-2y(a+b)+(a+b)_{2}$

$?-2x(a+b)-2y(b-a)=-2x(a-b)-2y(a+b)$

$?ax+bx+by-ay=ax-bx+ay+by$

$?2bx=2ay?bx=ay$