EQUATION OF THE LINE PASSING THROUGH THE POINT AND SUM OF INTERCEPT

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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