Misc 3

Transcript

Misc 3 Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively. Equation of a line by intercept form is 𝑥/𝑎 + 𝑦/𝑏 = 1 where a is x – intercept & b is y – intercept Given that sum of intercept is 1 i.e. a + b = 1 Product of intercept is − 6 i.e. a × b = − 6 From (1) a + b = 1 a = 1 – b Putting value of a in (2) a × b = − 6 (1 – b) × b = − 6 b – b2 = − 6 0 = b2 – b – 6 b2 – b – 6 = 0 b2 – 3b + 2b – 6 = 0 b(b – 3) + 2(b – 3) = 0 (b – 3) (b + 2) = 0 So, b = 3, & b = – 2 Hence a = − 2, b = 3 & a = 3, b = − 2 Now, finding equation of lines Hence, equation of lines are − 2x + 3y + 6 = 0 & 3x − 2y + 6 = 0