( 280 ) 



CHAPTER XVIII. 



TANGENT AND NORMAL TO A PLANE CURVE. 



257. DEFINITION. Let P, Q, be two points on a curve, 

 and suppose a straight line drawn through them ; the limit- 

 ing position of this straight line, as Q moves along the curve 

 and approaches indefinitely near to P, is called the tangent 

 to the curve at the point P. 



JUl Cr 



To find the equation to the tangent at a given point of 

 a curve. 



Let x, y, be the co-ordinates of the given point P, 



x + Ace, y + Ay, the co-ordinates of another point Q on the 

 curve. 



Then x, y y being current co-ordinates, we have for the 

 equation to the straight line PQ, 



y - y = 



9 ' 



y 



- 



,, 



( x - 



v 



that is, y'-y^^ ('-) 



Now let Q approach indefinitely near to P; the limit of 



