Question

11. 4 12 Match each equation with the name of the conic, its eccentricity and equation of directrix: Your answer should contain one letter from each column. [18pts) H. 4 T. X=-3 12 (a) r= A. Circle 3 J. U. y = 6 2-3cos 3 B. Ellipse K. W. y= 2 6 C. Hyperbola L. X. x = -4 8-8sin 2 D. Parabola M. 3 Y y=-12 18 (c) E. Cardioid 3 Z. y. 4+3 sin 2 R 1 (b) ra z con S. 6

Answer 1

12 2- 3 COSO 12 22 2 AHOIN coso 6 3 COS Now, compair with standard form ep directrix where is 응 x= -P I-ecoso Note that les 3 2 커 The conic is hyperbola. From the bumerator, 6 ep = 3 2 p = 6 2 P- 6* 3 p=4 directox is x = -4 Answer is N X

6 6 8-8 sino 6 8 8 sino 00100 8 3/4 sino comparing to standard form V ep - esince The directrix is YER . e al .. The conic is a parabola Nowy ep = 3, 4 1 x pa द pa 3 4 The directrix is 3 Answer is D IR IZ

© 18 4+3 sing T8 4 - 4 + since 9/ 1+ 3 4 sino ep comparing to Standard form. It e sino 3 e- ht 4 : The conic is an ellipse The directrix is y =p g Now , ep = ... pa 2 ps alt x U1 p= 36 . p=6 The directrix is y - 6 Answer is B J U