Oft-iao.1 rzz* cojr/4 </ IHHIB 218 



: equatioi i Art. 138 represents a circle, 



A m B, and then equation [54] becomes 



Q + mP 



!r*nf the diameter U ^ ; but the slope of the given 

 of chords to at, hence the diameter is perpendicular to its chords. 



4. By means of eq. [.V4], i*., by upecialixing its coefficient*, prove 

 the diameter of a circle passes through the center of the circle, 



9. By means of equation [.VI] prove that any diameter of the ellipse 

 SJT* + y - x + 2y = peases through the center of the ellipse, Does 

 this property belong to all ellipses? To all conies? 



6. Find the equation of that diameter of the hyperbola 



chords are parallel to the line y = 2x -f 10. Does this diameter 

 through the center of the curve? 



7. Fin,! the angle between the diameter and iU chorda in exorcise 6L 



& Show that every diameter f the parabola 3y* - 16x + 12 y = 4 

 U parallel to its axis. I.t this a property belonging to all parabolas? 



<?, by the method .. equation of that diameter 



the hyperbola x - 4 y + lOy + Ox - 15 = 0, which bisects chords 

 tothelinc3x-4y= 12. 



130. Equation of a conic that passes through the intcrsec- 

 of two given conies. 1 M\ -n < "iiica be 



-Cl-0, (1) 



Q-O; . . . (*2) 

 if AT be any constant \\ 1. 



o . f. a A 



a conic whose axes are parallel to the coordinate 

 (Art. 120), nnl \\hieh pusses through the i.j; 

 i the .9, = and <S^0 intersect each 



il): i.e., j9 t + ^aO represents * family <f conica, 

 mcinlHT ..f \\liich passes through the intersections of 

 and 8} 0. The parameter k may be so chosen that 



