//;> [CM. \ H. 



It is to be observed that (his e^nat i.n [ JnJ is not of the, 



form 



x* + f + 2Gz, -/ 



which was discussed in Art. 70; it differs from that equa- 

 ti.in in that it contains an xy-term. If. however, tin- i 

 rectangular, as in Art. 7'.', then c-oso) = 0, and equation 



] reduces to the standard form of Art. "'., vi/..: 



whicli is a special case of jnation [40]. 



100. The angle formed by two intersecting curves. lly ih 

 angle between two intersecting cnr\es is meant the ;r 

 formed hy the two tangents on.- to eaeh curve, dra\\n 

 through the point of intersection. 



Hence to find the angle at whicli two curves intersect, it 



is only necessary to lind the point of intersection, then to 



the equations of the tangents at this point, one to each 



curve, and finally to lind the angle formed by these tangents. 



EXERCISES 



1. Find the polar equation of the circle whose center is at the j 

 f?, ^j and whose radius is 10; determine also the points of its i 

 section with the initial line. 



2. Find the polar equation of a circle whose center is at the point 

 I 1"), | j and whose radius is 10. Find ato the equation* of the Ungeoti 

 to the circle from the pole. 



3. A circle of radius 3 is tangent to the two radii vectores which 

 make the angles 60 and 120 with the initial lino: find its polar fj 

 tion, and the distance of the center from the origin. 



4. Find the equation of a circle of radius 5, with center at the ] 

 (2, 3), if o> is 60. 



5. Find the equation of a circle of radius 2, with center at the or 

 if is 120. 



