NORMAL TO A CURVE. 281 



-r-^ is ~, and the equation to the tangent at P is 

 Aa; dx 



258. DEFINITION. The normal to a curve at any point is 

 a straight line draWn through that point at right angles to 

 the tangent at that point. 



To find the equation to the normal at any point of a curve. 



Since the equation to the tangent at the point (x, y) is 



the equation to the normal at the same point is 



dx 



supposing the axes rectangular. 



259. Let the tangent and normal at the point P meet the 

 axis of x at the points T and G respectively ; draw the ordi- 

 nate PM ; then 



MT is called the subtangent, 

 MG is called the subnormal. 



MP 



Now -^= the tangent of PTx 



_ 

 dx' 



therefore 



- = . 

 dy " ay 



dx 

 Also - = tangent of GPM tangent of PTx 



therefore MG = y -/ . 



y dx 



