Calendar: 1871-1872 Page 583

the school 583 If ffom any point Ο of chord Qq of parabola OR be drawn parallel to the diameter Pi' which bisects Qq meeting the parabola in prove that QO Oq SP R0 If OR be produced to meet the tangent at in then TR RO QO Oq From point Τ tangents TP and TQ are 'drawn to parabola and AT AP AQ meet the directrix in Τ' prove that TP rq If the normal to the ellipse at Ρ meet the major axis in and Pi be the ordinate of then NG NC PC2 AC2 If the normal meet the minor axis in G' and G'M be the perpendicular from G' on SP then Ρ Μ AC In the ellipse if SY S'Y' he the perpendiculars from on the tangent at then SY S'Y' BC2 If from the focus S' line be drawn parallel to SP it will meet the perpendicular iS Tin the circumference of circle Find when the perimeter of the quadrilateral formed by the tangent the perpendiculars and the transverse axis will be the greatest possible If CD be conjugate to CP then will CP be conjugate to CD Two conjugate diameters of an ellipse are cut by the tangent at any point in ΛΓ and prove that the area of the £ CQM varies inversely as that of the triangle CQN In the ellipse if Ρ Η be tbe chord of the circle of curvature through the centre then PH CP 2CBP The circles of curvature at the extremities of two conjugate diameters of an ellipse meet the ellipse again in respectively show that PR is parallel to DQ