:_ m I in 



6. The line y = .(*- a) passes through the (boos of the 



conic ^t** i OnwiMlH ..... i H* lie? Find the line join- 



Ing iU polo to th* relation exist* between thk line and 



the given focal chord? 



7. \N hit t h polar of the vertex of the con tc 



/ + c*a, 



ith reference to the curve? 



8. Uh.it :> the equation of each common chord of the two conic* 



16*<+B*= 144. 16x*-8/= 144? 

 HIM I > equation 3; find A- to that >, can be 



I.i.-!. : .1. 



9. I 'rove that the perpendicular dropped from any point of the 

 directrix, to the polar of that {- .int, paves through the focus 



.& the simplest standard equations of the conies, find for each 



10. the polar of the focus; 



11. tii.- IN,:,- <>f the directrix; 



12. the pole of each axis; and, for the llij.-- and hyperbola, the 

 polar of the center. 



13. T i tid a conic tli r. .* of the ellipse 4x*+f*=16 

 the parabola jr* = 4 z + 4, and also passing through the point 



a conic i> 



14. Show that the curves + = 1 =1 have the tame 



10 l I 



foci, and that they cut each other at right angles. 



15. I iml the vertices of an equilateral triai^!'- circa inscribed about 

 the ellii Ox* 4- 16 y* = 144, one side being parallel to the major axis 



curve. 



16. T in*l the normal to the conic 3x-Hy t -2r-jf = T ^, making the 

 angle tan-'( J) with the r-axU. 



17 Sho* thai ' ie locus of the pole, with respect to the parabola y* = 4 or, 

 of a tangent to the hyp.- y* = a, is the ellipse 4 x* + y* = 4 a 



18. Show that * + -.**.- = 1, where I: is an arbitrary con- 



jj -i 

 slant, represents an ellipse having the same foci as ' t "*" Vf ~ ^ when 



