EQUATION OF THE LINE PASSING THROUGH THE POINT AND SUM OF INTERCEPT
Equation of the Line Passing Through the Point and Sum of Intercept :
Here we are going to see finding equation of line passing through the point and sum of intercept is given.
Equation of the Line Passing Through the Point and Sum of Intercept - Examples
Question 13 :
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
Question 14 :
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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