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. 1867 Excerpt: ...= 2cx, 36. EC, CD are two arcs of a parabola, such thai the lengths of those parts of the diameters between their middle points E, F, and the curve are equal; prove that EF is parallel to the tangent at C. 37. Two equal parabolas have the same axis, and a chord, Qq of the one making a constant angle with the axis cuts ...
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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. 1867 Excerpt: ...= 2cx, 36. EC, CD are two arcs of a parabola, such thai the lengths of those parts of the diameters between their middle points E, F, and the curve are equal; prove that EF is parallel to the tangent at C. 37. Two equal parabolas have the same axis, and a chord, Qq of the one making a constant angle with the axis cuts the other in P; prove that PQ. Fq is constant. 38. If there are three tangents to a parabola, the triangle formed by their intersections is half that whose angular points are the points of contact. 39. If a circle be described with centre S, and radius SA, and any focal chord Pp cut this circle in Q, q, PQ.pq = a. 40. Find the locus of the vertex of a parabola which has a given focus and touches a given straight line. 41. In the radius vector SP, Q is taken equal to the semiordinate, find the locus of Q, 42. If PSp be a focal chord, I the semi-latus rectum, SP+SpV 43. If r, r- be two radii vectores at right angles to one another, I the semi-latus rectum, 44. If PM be the perpendicular on the directrix from P, SM' = ia.SP. 45. If Pp be a focal chord, prove that the triangle FApo=(Ppf, 46. If the tangent at Q be parallel to the focal chord Ppt. SP.Sp = 2l.SQ., . Y. G. 8 47. If Q be on the focal chord Pp, and. SQ=Pp, find the locus of Q. 48. PQ is a chord through a given point 0, cutting the parabola in PQ; prove that PO. OQ is least-when PQ is perpendicular to the axis. 49. The abscissae of two points on a parabola are 35, 3a;, and their focal distances r, 2r; determine their positions. 50. Given a diameter and its tangent, find the locus of the vertex. 51. Find also the locus of the focus. 52. The directrix is the polar of the focus. 53. The poles of all straight lines through the foot of the directrix lie on the latus rectum. 54. The pole...
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