Equation of line in Straight lines

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Question

$If the intercepts cut off on the coordinate axes by the line a x + b y + 8 = 0 are equal in length$
$but opposite in signs to those cut off by the line 2 x - 3 y + 6 = 0 on the co ordinate axes$ $respectively then 25 a + b =$

Moderate

Solution

$\begin{array}{l} - \frac{8}{a} = - 3, - \frac{8}{b} = 2 \\ \Rightarrow a = \frac{8}{3}, b = - 4 \\ 25 a + b = \frac{200}{3} - 4 = \frac{200 - 12}{3} = \frac{188}{3} = 62.67 \end{array}$

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