.1 \ i/. > //' rr i\ m. 



15. From any point on the latus rectum of a parabola, perpendiculars 

 are drawn to the tangents at its extremiti. , . -h..\\ that tin- lin.- 



the feet of these perpendiculars is a tangent to the parabola. 



16. If tangent* are drawn to the parabola y 2 = 4 ax from any 

 on the line x + 4 a = 0, their chord of contact will subtend a right 

 at the vertex. 



Two tangents of slope //< ami ?/<', respectively, are drawn to a parab- 

 ola ; find the locus of their intersection : 



17. if mm'= k\ 



19. ifl-.Uk 



m m 



20. Kind the locus of tho cantor of a oirrl^ which passes through a 

 given point, and touches a given line. 



21. The latus rectum of the parabola is a third proportional to any 

 abscissa and the corresponding ordinate. 



22. Find the locus of the point of inteixrtion of tangents dnr 

 points whose ordinates are in a constant ratio. 



23. What is the equation of the chord of the parabola y*= 3jc whose 



middle joint is at (2, 1)? 



24. A double ordinate of the parabola y* \px is 8 /> . pi 



tin- lines from the vertex to its two ends are perpendicular to ea< h otlu-r. 



25. Kind the locus of the center of a circle which is tangent to a ^ 

 circle and also to a given straight line. 



26. Kind the intersections of a normal to the parabola with the n 

 and the length of the intercepted portion. 



27. Prove that the locus of the middle point of the normal intercept. ! 

 between the parabola and its axis is a parabola whose vertex is the focus, 

 and whose latus rectum is one fourth that of the original parabola. 



28. Prove that two confocal parabolas, with their axes in opi 

 directions, intersect at right angles. 



29. Kind the equation of the parabola when referred to Ian 

 ', extremities of the latus rectum as coordinate axes. 



3O The product of the tangent and normal lengths for a certain point 

 of thn parabola y a = 4px is twice the square of the corresponding ordi- 

 nat- . find the point and the slope of the tangent line. 



