: ;///. /;/./. il>8* 



10 (.iven the ellipse 8* + 4f*12, find the conjugate diameters 



. |-.int whose eooentrie angle is JUI*. 



1 1 Kind the lengths of the diameters in exercise 10. 



12. The lengths of the chord joining the extremities of any two urn- 

 jugate diameters of the ellipse J + jj = 1 is V>+ 6* + oVsuiJ^ 

 Find its greatest value. What is the corresponding value of $? 



13. Theareaof a triangle inscribed in an ellipse, if ^, ^, ^ be the 

 eccentric angles of the vertices, is 



14. r.iven the point (-3, -1) on the ellipea * + Sy*= 12; find the 

 corresponding point on the major auxiliary circle, and also find the 

 eccentric angle of the given point. 



Kind the polar of the focus of an ellipse with reference to each 



16. Kind the pole of the directrix of the ellipse with reference to each 

 auxiliary circle. 



17. ProresiijdyticmJlythmtUngcnUatbeendsof aaychordinUnect 

 on the diameter which bisects that chord. 



157. Supplemental chords. The chords drawn from any poir: 

 an ellipse to the extremities of a diameter are called supplements! chords. 

 Such chords are always parallel to a pair of conjugate diameters, sin** 

 their slopes satisfy the relation 



For if P.^Ov y,) ami r, = (-r |t - V| ) be the extremities of a 

 diameter, and P* (i*, y) be any other point <>f th.- ellipse, and m and 

 m' the slopes of the chords //>, and /*/> respectively, 



~ f\ 

 fore 



But 



and 



