The ratio in which the line segment joining points A (a1, b1) and B (a2, b2) is divided by y-axis is

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Let P( 0 ,y) be the point of intersection of y-axis with the line segment joining` A(a_1 , b_1) " and B " (a_2 , b_2)` which divides the line segment AB in the ratio λ : 1 . Now according to the section formula if point a point P divides a line segment joining `A(x_1 ,y_1) " and" B (x_2 , y_2)` in the ratio m:n internally than, `P ( x, y) = ((nx_1 + mx_2)/(m+n) , (ny_1 +my_2)/(m + n))` Now we will use section formula as, `( 0, y) = ((λa_2 +a_1)/(λ + 1) , ( λb_2 + b_1) /(λ + 1))` Now equate the x component on both the sides, (λa_2 + a_1) /(λ + 1) = 0 On further simplification, λ = - a_1/a_2

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