7 in: 



-/ - .'"' 



OH the conic, and they are real anl i . f Q U outnJ* of 



conio. the above proposition but 



also tho fart that no n-al tangent can be drawn to a < 



an internal point, an<l that only one tangent can lie 

 a to a oo i a given ]M unt on the curve. 



12& Equation of a chord of contact. If the two tang* 



are lia\\n from an external point to a conic section, 

 straight lino through tho corre- 



I'lin^ point-> 



called the chord of contact 

 point i 



\\hi.-h !!. tangents are drawn 

 t. 90). 



; Op i, ;o ex- 



al point from \\hirli 

 t\\o tangents are dra\\n; 7*,= 



and TI & Or // a ). 

 points of tan-.-n.-y of tin-so tangents to the conio whose 

 aquation 



Aj*+ Bf -f 2'? _' rv+^zaO; . (1) 



;iiiivil to lin.l tho tMjiiation of tlio lino through T % 

 an. I T v 



11 of tho tun^rnt at T., T.-f. Art. 1'2'2) is 

 %y-f G(jr + x.i )+/'(// 4- y s )-fC-0, . . . (2) 



tion of tho taiiL." is 



Ar^r -f By^y -f Q (f -f- j- 8 ) -h F(y -4- y t ) -f C 0. . . . (8) 

 > a.h of 1 1 iose tangents, l.\ hyjHthesis, passes tin 

 .for.> tli,- roonlinates jfj and y t satisfy Loth conation 

 . 



r -ny f )-fC-o....(4) 

 i r a + A'/i V 8 4- ^(*i + *3> * -^(jfi -I- ^i > + C' - 0. (5) 



