282 PERPENDICULAR FROM ORIGIN ON TANGENT. 



In these expressions for the subnormal and subtangent, 

 it is to be observed that the subtangent is measured from M 

 towards the left, and the subnormal is measured from M 



towards the right. If in any curve y -~ is a negative quantity, 



CKC 



it indicates that G lies to the left of M, and, as in that case 



doc 

 y ,- is also negative, 2* lies to the right of M. 



260. In the equation to the tangent put y = 0, then 

 , da; 



/y . /y __ A/ _ 

 JU JU U -, . 



9 dy 



this therefore is the value of OT. 

 Similarly, if we put x = 0, we find 



which gives the ordinate of the point where the tangent 

 meets the axis of y. 



261. The length of the perpendicular from the origin on 

 the tangent is, by the usual formulae of analytical geometry, 



dy 







dx 



262. If the equation to a curve be given in the form 

 $ ( x > y} = > we nave j by Art. 177, 



dy _ \dxj 

 dx 



Thus the equation to the tangent becomes 

 , , . fd<j>\ . , . fd<f> 



V-^^+K-** 



and the equation to the normal becomes 



