Find the equation of the straight line which passes through the point (1, –2) and cuts off equal intercepts from axes.

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Vishal Baghel | Contributor-Level 10

a year ago

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} I n t e r c e p t f o r m o f s t r a i g h t l i n e \\ \frac{x}{a} + \frac{y}{b} = 1, w h e r e a a n d b a r e t h e o n t h e a x i s \\ G i v e n t h a t a = b \\ ∴ \frac{x}{a} + \frac{y}{a} = 1 \dots (i) \\ I f e q n . (i) p a s s e s t h r o u g h t h e (1, - 2), w e g e t \\ \frac{1}{a} - \frac{2}{a} = 1 \Rightarrow - \frac{1}{a} = 1 \Rightarrow a = - 1 \\ S o, t h e e q u a t i o n o f t h e s t r a i g h t l i n e i s \\ \frac{x}{- 1} + \frac{y}{- 1} = 1 \Rightarrow x + y = - 1 \Rightarrow x + y + 1 = 0 \\ H e n c e, t h e r e q u i r e d e q u a t i o n i s x + y + 1 = 0 . \end{array}$

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