Till; ANGLE BETWEEN A LINE AND CURVE 133 



The slope of the line = m, and hence m = tan 2 . This gives 

 the inclination of the line KL. 



Then PCL =$1-^ 



Example. Find the angle between the curve xy = 1 and the 

 straight line y = 2x + 1 at the point of intersection. 



xy= 1 



x (2x + 1) = 1 



2x 2 + x 1 = 



(20-1X0+1) = 



or x = - and x = 1 







There are two points of intersection : A, whose co-ordinates 



are -, 2 ; B, whose co-ordinates are 1, 1. The slope of the 



I 



line is 2, and hence the inclination of the line is tan -1 2 = 63 26'. 

 For the curve = x~ l 



and 



dy 



Inclination of the tangent to the curve is tan -1 ( ^ j 





