If (a2 + b2)(x2 + y2) = (ax + by)2; prove that: ax=by. - Mathematics

If (a² + b²)(x² + y²) = (ax + by)²; prove that: `a/x = b/y`.

Sum

Given that, (a² + b²)(x² + y²) = (ax + by)²

a²x² + a²y² + b²x² + b²y² = a²x² + b²y² + 2abxy

a²y² + b²x² – 2abxy = 0

(ay – bx)² = 0

ay – bx = 0

ay = bx

`a/x = b/y`

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