Q13 of 319 Page 23

The slope of a line is double of the slope of another line. If tangents of the angle between them is , find the slopes of the other line.

Given, The tangent of the angle between them is

To Find Slope of the other line.


Assumption: The slope of line m1 = x, and m2 = 2x


Formula used:


Explanation: We have tan given, then



Case 1:



2x2 + 1 = 3x – 6x


2x2 + 3x + 1 = 0


2x2 + 2x + x + 1 = 0


2x(x + 1) + 1(x + 1) = 0


(2x + 1)(x + 1) = 0


x = – 1,


Case 2:



2x2 + 1 = 3x


2x2 – 3x + 1 = 0


2x2 – 2x – x + 1 = 0


2x(x – 1) – 1(x – 1) = 0


(2x – 1)(x – 1) = 0


x = 1,


Hence, The slope of other line is either 1, or – 1, .


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