# 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

#### 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