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Distance between Two Points on the Same Coordinate Axes

Prove that ...

Question

Prove that $x = \frac{a^{2} + a b + b^{2}}{a + b}, y = \frac{a b}{a + b}$ is solution of the equation $b x - a y = b^{2}$

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Solution

$\begin{matrix} x = \frac{a^{2} + a b + b^{2}}{(a + b)}, y = \frac{a b}{(a + b)} P u t t i n g V a l u e o f x a n d y i n b x - a y = b^{2} \Rightarrow b [\frac{a^{2} + a b + b^{2}}{a + b}] - \frac{a^{2} b}{(a + b)} = b^{2} \Rightarrow \frac{a^{2} b + a b^{2} + b^{3} - a^{2} b}{(a + b)} \Rightarrow \frac{a b^{2} + b^{3}}{(a + b)} \Rightarrow b^{2} \frac{(a + b)}{a + b} = b^{2} p r o v e d . H e n c e, V a l u e o f x a n d y s a t i s f y t h e e q u a t i o n b x + a y = b^{2} . \end{matrix}$

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Distance between Two Points on the Same Coordinate Axes

Standard X Mathematics

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