5^8.] 





151 



i- tin- j.... , < n the circle 



s 



at 1 + if r* the M ubuiigeiit &-, the tangent length 



'i 

 3o, the Mubnortiml = x r and uml length r. 



Tin- .l.-ii\.ii;..j "f tli.-.sr values in left as an exercise for the 



lent, .M is also tl.- <l<-riv.iii<n .f the coire*!' >i 

 r\|.ri-*si,,ns f,,r tin* rin-lo 2* -I- ^ -f 2 (? * + 2 1> 4- C - 0, the 

 i "f contact being (r r //,). 



EXERCISES 



Find the lengths of the tangent, subUngent, normal, and toboormal, 

 l lie circle z*-*- y-3x-f lOy = 15; 



2. for the point ( l.e circle x + y* - 10 x = 0; 



3. fur the point whoM abecima in V7 on the circle T* + y = 25. 



4. The fttibtangent for a certain point on a circle, whoae center b at 

 the origin, is 5J, and iu subnormal U 3. Find the equation of the circle, 

 ami the point of tangency. 



8& To find the length of a tangent from a given external 

 point to a given circle. I^et Pjs(jr p yj) be the giv.-n 

 : n.il point, ami let 



be the gi\< n . ircle. The center of this circle (Art. 79) is 

 ("0, ~F), and its radius is 



\ li- . /" ''. .l'in /'jt.. tin- 



center A'. h\i\\ the tangent 

 7*!<?, and also the radius JTQ. 



(A 



i . . ... 



(Art. 79) 



