Question:
Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and - 6, respectively.
Answer:
Equation of straight line in intercept form is
x/a + y/b = 1 ...........1
where a and b are the intercept in x and y-direction respectively
Now given that
a+b = 1 and a*b = -6
(a-b)2 = (a+b)2 - 4ab
= 1 - 4*(-6)
= 1+ 24
= 25
=> a-b = √25
=> a-b = 5,-5
Case1: a+b = 1 and a-b = 5
After solving it, we get
a = 3, y = -2
Case2: a+b = 1 and a-b = -5
After solving it, we get
a = -2, y = 3
From equation 1, put the value of a and b, we get the equation of line which are:
x/3 - y/2 = 1 and -x/2 + y/3 = 1
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