Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 Excerpt: ... ax again at Q; if x1 is the abscissa of P, prove that PQ2 =--(#i + »)3 28. In the parabola y2 = 4cax, show that sly--Aax1 is the projection of the tangent from (xv y) to the curve upon the tangent at the vertex. 29. Perpendicular lines AP, AQ are drawn from the vertex of a parabola to meet it in P, Q: prove that the normals at P and Q intersect on a 30. TPZ is a tangent at P to a parabola cutting the axis of the curve at T, and PZ is taken in a constant ratio to TP; prove that the locus of Z is a parabola, and find its parameter (latus rectum). Revision Questions on the Parabola. These may be taken orally, or the answers may be written down without any working. What are the equations of the directrices of the following parabolas: 1. y2--4aa?. 2. y'2 =-&ax. 3. x2--ay. 4# x2=-4:ay. 5. ax2 + by = 0. 6. ax2--by. Give the co-ordinates of the vertices of the parabolas: 7. y2 = 4:ax + u). 8. x2 = Say-2a). 9. y-kf = ±ax-h). 10. x + h)2=-.ay + k). 11. y + k)2 = 2ah-x). 12. (x-3)2 + 2/ = 0. What is the equation of the latus rectum of the parabola: 13. y2 = 4:ax. 14. y2--2ax. 15. y2=-2a,x. 16. x2 = 4ay. 17. x2=-4:ay. 18. x2 = Say. What are the co-ordinates of the focus of the parabola: 19. y2=-ax. 20. x2 = ay. 21. x2=-ay. Give the equation of the axis of the parabola: 22. x2 = by. 23. x2 =-4y. 24. y-k)2 = 4=a(x-h). 25. x + h)2=4ay-k). 26. x-2)2 = 4y. 27. y2=±x-3). 28. If y2--4:ax, y--±2slax; what do you deduce as to the shape of the curve? Give the equation of the tangent at the point (xl9 yj to the following curves: 29. x2 = 4ay. 30. y2=-±ax. 31. ax2 + by = 0. 32. ax2 = 4:by. In each of the following curves, give the equation of a tangent in terms of its slope: 33. y2 = Sax. 34. y2=-±ax. 35. ay2 = bx. 36, x2 = 4ay. 37. What is the e...
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