Q10 of 319 Page 24

Show that the tangent of an angle between the lines and is .

Given:


……(i)


……(ii)


To prove:


The tangent of an angle between the lines and is


Concept Used:


Angle between two lines.


Assuming:


m1 and m2 be the slope of the lines (1) and (2), respectively.


Explanation:


∴m1, m2


Let θ be the angle between the lines (1) and (2).


∴






Hence proved, the tangent of the angles between the lines is .


More from this chapter

All 319 →
8

Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.

 9

Show that the line a2x + ay + 1 = 0 is perpendicular to the line x – ay = 1 for all non-zero real values of a.

 1

Find the values of α so that the point P(α 2, α) lies inside or on the triangle formed by the lines x – 5y + 6 = 0, x – 3y + 2 = 0 and x – 2y – 3 = 0.

 2

Find the values of the parameter a so that the point (a, 2) is an interior point of the triangle formed by the lines x + y – 4 = 0, 3x – 7y – 8 = 0 and 4x – y – 31 = 0.