J44 



ANALYTIC GEOM 



[Ca vii. 



as before, which is, for all values of //*, tangent to the circle whose 

 center is at the point (-(7, ~F) and whose radius is VG* + /** - C. 



NOTE 2. Because of its frequent occurrence, it is useful to memorize 

 equation [:W]. On tin- othrr hand, it is not recommended that equation 

 [:U] be memorized, but it should be carefully worked out by the stud. m. 

 Instead of employing either of these formulas, however, the stud.-m 

 may always attack the problems directly, as was done in An 



EXERCISES 

 Kind the equations of the lines which are tangent: 



1. to the circle z* + y a = 16, and \\lm-c >!<.JM- i 



2. to the circle * 2 + y 2 = 4, and which are parallel to the line x 

 + 3=0(cf. Ex. 1, Art. 82); 



3. to the circle x 2 + y a = 9, and which make an angle of 60 with the 

 z-axis; with the y-axis; 



4. to the circle x 2 + y 2 = 25, and which are perpendicular to the line 

 joining the points (~3, 7) and (7, 5) ; 



5. to the circle x 2 + y a = 2 x + 2 y - 1, and whose slope is -1. 



84. Equation of tangent to the circle in terms of the coordi- 

 nates of the point of contact : the secant method. 



(a) Center of the circle at the origin. Let P 1 =(a: 11 y } ) l>e 

 the point of. tangency, on the given circle 



^ + y = r. . . . (1) 



Through P l draw a secant line LM, and let P 2 = (x* # 2 ) 

 be its other point of intersection with the circle. If the 



point P 2 moves along the circle 

 until it comes into coincidence 

 with P,, the limiting position of 

 the secant LM is the tangent 

 P,T. (Art. 81.) 



The equation of the line LM is 



-*!).... 





Fio.ee. 



If now P 2 approaches P l until 



