142 PRACTICAL MATHEMATICS 



(12) Find the values of the radius of curvature of the curve 

 y = 3-2 + 1-7&B 1 ' 75 at the points where x = 1, as = 2, and x = 3. 



(13) The curve y = a+ to 1 ' 5 passes through the points (1, 1-82) 

 and (4, 5-32). Find a and b. Find the value of the radius of 

 curvature at the point where x = 2 ; find also the co-ordinates of 

 the centre of curvature for that point. 



(14) The curve y = a + be? passes through the points (0, 28-62), 

 (1, 35-70), and (2, 49-81). Find a, b, and c. Find the value of 

 the radius of curvature at the point where x = 1. 



(15) The curve y = ICte* is cut by the line y = 2x 10. Find 

 the co-ordinates of that point of intersection for which y is posi- 

 tive. Find the angle between the curve and the line at that 

 point. (B. of E., 1913.) 



(16) Find the values of the radius of curvature of the ellipse 



a? 2 w 2 



+ 2- = 1 at the points where x = and x 4. 



- ) J.U 



(17) Find the value of the radius of curvature of the curve 

 xy = 4 at the point where x = 2. Find also the co-ordinates of 

 the corresponding centre of curvature. 



(18) Find the co-ordinates of the point of inflexion on the 

 curve 4g/ = 6x z x*. 



(19) Find the co-ordinates of the point of inflexion on the 

 curve y = e~* . 



