A straight line passes through the point P( ₂ 16 , ₃ 27) such that the portion of the line intercepted between the co-ordinate axes is divided by P in the ratio 1:2 internally (starting from the x -axis). Then the equation of the line is:

Step-by-step solution

The coordinates of the point P are given by ( ₂ 16, ₃ 27) . Since ₂ 16 = ₂ (2^4) = 4 and ₃ 27 = ₃ (3^3) = 3 , the point is P(4, 3) . Let the line intersect the x -axis at A(a, 0) and the y -axis at B(0, b) . It is given that P(4, 3) divides the line segment AB internally in the ratio 1:2 . Using the section formula, the coordinates of P are: x = 1(0) + 2(a) 1 + 2 = 2a 3 y = 1(b) + 2(0) 1 + 2 = b 3 Equating these to the coordinates of P(4, 3) : 2a 3 = 4 2a = 12 a = 6 b 3 = 3 b = 9 The intercepts of the line are a =