Example 1 :
Find the equation of the straight line passing through the point (3, 4) and has intercepts which are in the ratio 3 : 2.
Solution :
Since the intercepts are in the ratio 3 : 2,
x-intercept(a) = 3k and y-intercept(b) = 2k
(x/a) + (y/b) = 1
(x/3k) + (y/2k) = 1
The straight line is passing through the point (3, 4)
(3/3k) + (4/2k) = 1
(1/k) + (2/k) = 1
(1 + 2)/k = 1 ==> 3/k = 1 ==> k = 3
a = 3k = 9, b = 2k = 6
Equation of the line :
(x/a) + (y/b) = 1
(x/9) + (y/6) = 1
(2x + 3y)/18 = 1
2x + 3y = 18
2x + 3y - 18 = 0
Example 2 :
Find the equation of the straight lines passing through the point (2, 2) and the sum of the intercepts is 9.
Solution :
Sum of intercepts = 9
a + b = 9
a = 9 - b
(x/a) + (y/b) = 1
(x/(9-b)) + (y/b) = 1
The straight line is passing through the point (2, 2)
(2/(9-b)) + (2/b) = 1
[2b + 2(9 - b)]/[b(9-b)] = 1
(2b + 18 - 2b)/(9b-b²) = 1
18 = 9 b - b²
b² - 9 b - 18 = 0
(b - 3) (b - 6) = 0
b - 3 = 0 b = 3 a = 9 - 3 ==> 6 (x/a) + (y/b) = 1 (x/6) + (y/3) = 1 x + 2y = 6 x + 2y - 6 = 0 |
b - 6 = 0 b = 6 a = 6 - 3 ==> 3 (x/a) + (y/b) = 1 (x/3) + (y/6) = 1 2x + y = 6 2x + y - 6 = 0 |
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