208 i.\. i/.>//< pjTOJtj rsr [en. \ in. 



Equations ( 1 ) ;ui<l (.".), respectively, assert that the points 



T a 3 r^y,) and 2^ 

 are each on the locus of tin? r<piaii<>n 



f'i' /' //i// + <?( + O5i) + F(y + yi) + C = O. . . [ >-' ") 



liui relation [52] is of the tirst degree in the two vari- 

 ables x and y, hence (Art. 57) its locus is a straight line; 

 i.., [;">-] is the equation of the straight line through !T a and 

 T \vhic -h wjis to be found. 



1. The equation [f>2] ot the chord of contact corresponding to 

 a given external point (r,, y,), and the equation [50] of the tangent 

 whose point of contact is (x,, y,) are identical in form. This mi-lu 

 been expected because the tangent is only a special case of the chord of 

 contact, since the chord of contact, for a given point, approaches more 

 and more nearly to coincidence with a tangent when the point is tak-n 

 more and more nearly on the curve. 



NOTE 2. The present article furnishes another method of treatment 

 for the question of Art. 124. To get the equations of the two tangents 

 that can be drawn through a given external point to a given conic, it is 

 only necessary to write the equation of the chord of contact corres]><>u<l- 

 ing to this point; then find the points in which this chord of contact 

 intersects the conic. These are the points of contact of the required 

 tangents, whose equation may then be written down. 



EXERCISES 



1. By first finding the chord of contact (Art 126) of the tangents 

 drawn from the point (~f, V) to the conic 



find the points of contact, and then write the equations of the tangents 

 to the conic at these points; verify that these two tangents interne* t in 

 the point (-}, y). 



2. Solve Ex. 1 by the method of Art 124. 



3. Solve Ex. 1 by the method of Art. 83, using equation [11]. 



4. Find the equation of a normal through the point (7, 5) to the 



con 10 



_ 4x + y* + 24* - 2y + 17 = 4. 



