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a/x - b/y = 0

ab²/x - a²b/y = a² - b²

solve using cross multiplication method

$T h e g i v e n e q u a t i o n b e a s, \frac{a}{x} - \frac{b}{y} = 0 ....... (1) \frac{a b^{2}}{x} - \frac{a^{2} b}{y} = a^{2} - b^{2} ...... (2) N o w, b y c r o s s m u l t i p l i c a t i o n m e t h o d, w e h a v e, \frac{\frac{1}{x}}{- b (- a^{2} + b^{2}) + 0 \times a^{2} b} = \frac{\frac{1}{y}}{0 \times a^{2} b - a (- a^{2} + b^{2})} = \frac{1}{a (- a^{2} b) + b (a b^{2})} \Rightarrow \frac{\frac{1}{x}}{- b (- a^{2} + b^{2})} = \frac{\frac{1}{y}}{- a (- a^{2} + b^{2})} = \frac{1}{a b (- a^{2} + b^{2})} \Rightarrow \frac{\frac{1}{x}}{- b} = \frac{\frac{1}{y}}{- a} = \frac{1}{a b} \Rightarrow \frac{\frac{1}{x}}{- b} = \frac{1}{a b} a n d \frac{\frac{1}{y}}{- a} = \frac{1}{a b} \Rightarrow \frac{1}{x} (- a b) = b a n d \frac{1}{y} (- a b) = a \Rightarrow x = - a a n d y = - b$

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