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If (A^2 + B^2)(X^2 + Y^2)` = (Ax + By)^2 ; Prove that `A/X = B/Y - Mathematics

If `(a^2 + b^2)(x^2 + y^2)` = (ax + by)^2 ; prove that `a/x = b/y`

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Solution

`Given (a^2 + b^2)(x^2 + y^2) = (ax + by)^2`

`a^2 x^2 + a^2y^2 + b^2x^2 + b^2y^2 + b^2y^2 + 2abxy`

`a^2y^2 + b^2x^2 - 2abxy = 0`

`(ay - bx)^2 = 0`

ay - bx = 0

ay = bx

`a/x = b/y`

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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 7 Ratio and Proportion (Including Properties and Uses)
Exercise 7 (C) | Q 9 | Page 101
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