Get live Maths 1-on-1 Classs - Class 6 to 12

Miscellaneous

Misc 1
Important

Misc 2 Important Deleted for CBSE Board 2023 Exams

Misc 3 Important You are here

Misc 4

Misc 5

Misc 6 Important

Misc 7

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12 Important

Misc 13

Misc 14

Misc 15 Important

Misc 16 Important

Misc 17

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21 Important

Misc 22 Important

Misc 23

Misc 24 Important

Last updated at March 22, 2023 by Teachoo

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 For b = 3 From (1) a + b = 1 a + 3 = 1 a = 1 – 3 a = −2 For b = –2 From (1) a + b = 1 a – 2 = 1 a = 2 + 1 a = 3 Hence a = −2, b = 3 & a = 3, b = −2 Now, finding equation of lines For a = −2, b = 3 𝑥/𝑎 + 𝑦/𝑏 = 1 𝑥/( −2) + 𝑦/3 = 1 (3𝑥 − 2𝑦 )/( −6 ) = 1 3x − 2y = − 6 −3x + 2y = 6 For a = −2, b = 3 𝑥/𝑎 + 𝑦/𝑏 = 1 𝑥/( −2) + 𝑦/3 = 1 (3𝑥 − 2𝑦 )/( −6 ) = 1 3x − 2y = − 6 −3x + 2y = 6 For a = −2, b = 3 𝑥/𝑎 + 𝑦/𝑏 = 1 𝑥/( −2) + 𝑦/3 = 1 (3𝑥 − 2𝑦 )/( −6 ) = 1 3x − 2y = − 6 −3x + 2y = 6 Hence, equation of lines are −3x + 2y = 6 & 2x − 3y = 6