Find the equations of the lines, which cut-off intercepts on the axes

1.	Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively
Answer» Let the intercepts cut by the given lines on the axes be a and b. It is given that It is given that a + b = 1 ………………..… (1) ab = –6 …………………….. (2) On solving equations (1) and (2), we obtain a = 3 and b = –2 or a = –2 and b = 3 It is known that the equation of the line whose intercepts on the axes are a and b is Case I: a = 3 and b = –2 In this case, the equation of the line is –2x + 3y + 6 = 0, i.e., 2x – 3y = 6. Case II: a = –2 and b = 3 In this case, the equation of the line is 3x – 2y + 6 = 0, i.e., –3x + 2y = 6. Thus, the required equation of the lines are 2x – 3y = 6 and –3x + 2y = 6.

Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively

Answer»

Let the intercepts cut by the given lines on the axes be a and b. It is given that

It is given that
a + b = 1 ………………..… (1)
ab = –6 …………………….. (2)
On solving equations (1) and (2), we obtain

a = 3 and b = –2 or a = –2 and b = 3

It is known that the equation of the line whose intercepts on the axes are a and b is

Case I: a = 3 and b = –2
In this case, the equation of the line is –2x + 3y + 6 = 0, i.e., 2x – 3y = 6.

Case II: a = –2 and b = 3
In this case, the equation of the line is 3x – 2y + 6 = 0, i.e., –3x + 2y = 6.
Thus, the required equation of the lines are 2x – 3y = 6 and –3x + 2y = 6.

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