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Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axis whose sum is 9. |
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Answer» Let equation of the line is \(\frac{x}{a} + \frac{y}{b}\) = 1 ______(1) Given a + b = 9 Since (1) passes through (2, 2) we have; \(\frac{2}{b} + \frac{2}{b}\) = 1 ⇒ 2a + 2b – ab ⇒ 2 (a + b) = ab ⇒ 18 = ab. Then the numbers are 3 and 6. Hence the equation of the line is \(\frac{x}{3} + \frac{y}{6}\) = 1 ⇒ 6x + 3y = 18 ⇒ 2x + y = 6 OR \(\frac{x}{3} + \frac{y}{6}\) = 1 ⇒ 3x + 6y = 18 ⇒ x + 2y =6. |
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