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Question
Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes
(i) equal in magnitude and both positive,
(ii) equal in magnitude but opposite in sign.
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Solution
(i) Here, a = b
So, the equation of the line is
\[\frac{x}{a} + \frac{y}{b} = 1\]
\[ \Rightarrow \frac{x}{a} + \frac{y}{a} = 1\]
\[ \Rightarrow x + y = a\]
The line x + y = a passes through (5, 6).
\[\therefore 5 + 6 = a\]
\[ \Rightarrow a = 11\]
Hence, the equation of the line is \[x + y = 11\]
(ii) Here, b = \[-\] a
So, the equation of the line is
\[\frac{x}{a} + \frac{y}{b} = 1\]
\[ \Rightarrow \frac{x}{a} + \frac{y}{- a} = 1\]
\[ \Rightarrow x - y = a\]
The line x\[-\] y = a passes through (5, 6).
\[\therefore 5 - 6 = a\]
\[ \Rightarrow a = - 1\]
Hence, the equation of the line is \[x - y = - 1\]
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