14-2 AffM.Y n< <-/ <M// //;r [Cii. \ II. 



EXERCISES 

 Kind the equations of the tangents: 



1. to the circle z* + y 8 = 4, parallel to the line r + 2y-f3 = 0; 



2. to the circle 3(z 8 -f y 2 ) = 4 y, perpendicular to the line x + y = 7 ; 



3. to the circle x 8 + y 1 + 10*- 6y - 2 = 0, parallel to th.- I'm,- 

 y = 2*-7; 



4. to the circle z 8 + y 8 = r 8 , and forming with the ares a ti 

 whose area is r 8 . 



5 Show that the line y = x + cViJ is, for all values of c, 1 m^-'nt to 

 circle x 2 -f y 8 = c a ; and find, in terms of c, the point of contact. 



6. Prove that the circle z 8 + y 8 + 2x + 2y + l=0 touches both 

 coordinate axes ; ami tiiul the points of contact. 



7. For what values of c will the line 3ar 4y-f c = touch the 

 circle * 8 + y a - 8x + 12y - 44 = 0? 



8. For what value of r will the circle a: 1 + y 2 = r 8 touch th- line 

 y = 3*-5? 



9. Prove that the line ax = b (y b) touches the circle x (x a) 

 + y (y 6) =0; and find the point of contact. 



10. Three tangents are drawn to the circle x 8 + y 2 = 9; one of lln-in 

 is parallel to the ar-axis, and together they form an equilateral triangle. 

 1 md their equations, and the area of the triangle. 



83. Equation of tangent to the circle a? 2 -f f/* = r* in terms 

 of its slope. The equation of the tangent to a given circle, 

 in terms of its slope, is found in precisely the same way as 

 that followed in solving (1) of Art. 82. Let m be the 

 given slope of the tangent, then the equation of the tangent 

 is of the form 



y = mx \-b, . . . (1) 



wherein b is a constant which must be so determined that 

 line (1) shall intersect the circle 



x a + / = r=' ... (2) 

 in two coincident points. 



