ANM. ) //' >,i.Mi-:i I;Y [( ii. ix. 



EXERCISES 

 1 Con-inict a parabola with focus 2 em from the directrix. 



2. Construct a parabola with hit us rectum equal to 6. 



3. Fiml tli {nations of the two tan-.-nl.-. to tin- parabola y* = 4/MC, 



which form with the tan^-nt at tin- vertex a circum>crihed equilat.-ral 

 tri.in-le. Kind also the ratio of the area of this triangle to the area of 

 tip- triangle whose vertices are the points of tangency. 



4 rind the equation of a tangent to the parabola y a = 4px, perpen- 

 dicular to the line 4y - x + 3 = 0, ami find its point of contact. 



5. Find the equations of the two tangents to the parabola y 8 = 5* 

 from the point ( 1,1). using formula [.">(']. 



6. Write the equations of the tangents to the parabola y a = 1 



the extremities of the latus rectum. < >n what line do these tangents 

 intersect? (cf. Art. L88 (6), p. L'JS.) 



7. Write the equations of the tangent and normal to the parabola 

 y = 9x, at the point (1. <,). 



8. Write the equation of the normal to the parabola y* = 6x, drawn 

 through the point (. > ) 



9. Writ- the equation of the tangent to the parabola y a = 4/>/. for 

 the }K)int for which the normal length equals twice the tangent : for the 

 point for which the normal length is equal to the difference between the 

 subtangent and subnormal. 



10. Two equal parabolas have the same vertex, and their axes are at 

 ri^ht angles: find the equation of their common tangent, and show that, 



oints of contact are each at the extremity of a latus rectum. 



11. Find the locus of the middle point of the normal length of the 

 parabola y* = 4px. 



12. The subtangent of a parabola for the point (:.. 1) is 10; find the 

 equation of the curve, and length of the subnormal. 



13. Find the subtaugent, and the normal length, for the point whoso 

 abscissa = -6, and which is on the parabola y 2 = -6 x. 



14. Find the equation of the tangent parallel to the polar of (-1. -') 

 with respect to the parabola y* = 12 x\ also find the point of contact, 

 the length of the tangent, and the subtangent 



15. Find the equation of a parabola which is tangent to 2 y 3 x = 1, 

 whose vertex is at the origin, and whose axis is parallel to the z-axis. 



