Algebraic Geometry

W.M. Baker

Editorial: Lightning Source UK Ltd 2012-05-18, 2012
ISBN 10: 1236134516 / ISBN 13: 9781236134516
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Sinopsis: 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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Detalles bibliográficos

Título: Algebraic Geometry
Editorial: Lightning Source UK Ltd 2012-05-18
Año de publicación: 2012
Condición del libro: New

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W. M. Baker
Editorial: RareBooksClub
ISBN 10: 1236134516 ISBN 13: 9781236134516
Nuevos Paperback Cantidad: 20
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Descripción RareBooksClub. Paperback. Estado de conservación: New. This item is printed on demand. Paperback. 68 pages. Dimensions: 9.7in. x 7.4in. x 0.1in.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. y2 - and 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 4a(x-h). 25. x h)24ay-k). 26. x-2)2 4y. 27. y2x-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. . . This item ships from La Vergne,TN. Paperback. Nº de ref. de la librería 9781236134516

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