Q17 of 59 Page 178

Find the equation of the line which passes through the point (– 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.

Let AB be a line passing through a point (-4, 3) and meets x – axis at A (a, 0) and y – axis at B (0, b)

Using the section formula for internal division, i.e.


…(i)


Here, m1 = 5, m2 = 3


(x1, y1) = (a, 0) and (x2, y2) = (0, b)


Putting the above values in the above formula, we get




⇒ -32 = 3a or 24 = 5b


or


Intercept form of the line is



Putting the value of a and b in above equation, we get





⇒ -72x + 160y = 768


⇒ -36x + 80y = 384


⇒ 18x – 40y + 192 = 0


⇒ 9x – 20y + 96 = 0


Hence, the required equation is 9x – 20y + 96 = 0


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