II. Thr 



Special Equati..,, >f the Second Degree 

 + 2 Gx + 2/ + C = 



100. The elUpee defined ......... 179 



110. The first standard equation of the ellipse .... 180 



111. To trace the ellipae ** + =l ...... 182 



a* ft 1 



11.'. Intrinsic property of the ellipse. Second standard equation . 183 



113. Every equation of the form 



Ax 9 + By* + 2 Gx + 2Fy + C = 



repreaenU an ellipse whose axes are. parallel to the coordi- 

 nate axes, if A and B have the same sign .... 186 



114. Reduction of the equation of an ellipse to a standard form . 189 



III. The 

 Special Equation of the Second Degree 



Ax* - By* + 2 Gx + 2Fy + C = 

 The hyperbola defin. .1 ........ 190 



1 16. The first standard form of the equation of the hyperbola . 191 



117. To trace the hyperbola ~-f'=l ...... 193 



fl* Or 



118. Intrinsic property of the hyperbola. Second standard equa- 



tion .......... 195 



119. Every equation of the form 



Ax* + By* + 2 Gx + 2 Fy + C = 



represents an hyperbola whose axes are parallel to the coor- 

 dinate axes, if A and B have unlike signs . . . . U7 



120. Summary .... ..... 199 



IV. T<tngcntt t Xormal*, Polart, Diameters, etc. 



121. Introductory .......... 200 



122. Tangent to the conic Ax* -f By 3 + 2Gx + 2Fy+C = Q in 



terms of the coordinates of the point of contact : the secant 



method ........... 200 



128. Normal to the conic Ax* + By* -f 2 Gx + 2Fy + C = 0, at a 



given point .......... 203 



124. Equation of a tangent, and ot a normal, that pass through a 



given point which is not on the conic ..... JuO 



