# Calendar: 1878-1879 Page 598

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596 GENERAL LITERATURE AND SCIENCE 17 If the tangent to the parabola at any point Ρ intersect the directrix in then SZ is at right angles to SP 18 If the tangent at any point Ρ intersect the tangent at the vertex in then SY will bisect Ρ Τ at right angles and will be mean proportional between SA and SP 19 If circle be described about the triangle SPN the tangent to it from $PN 20 The tangent at any point of parabola meets the directrix and latus rectum produced in points equally distant from the focus 21 Draw pair of tangents to parabola from an external point 22 If QV be an ordinate to the diameter PV then QV2 ASP PV 23 Find the equation to the parabola referred to tangents at the ends of the latus rectum as axes 24 If chord of the parabola iax be tangent of the parabola 8a -e then the straight line χ bisects that chord 25 The sum of the distances of any point from the foci of an ellipse will be less or greater than the axis major according as the point is inside or outside the ellipse 26 The tangent to the ellipse at any point makes equal angle3 with the focal distances 27 If PQqP' be chord of the auxiliary circle and circle be described on the minor axis as diameter cutting the chord in and then PQ Pq CS2 28 If from the foci and S' SY and S"Y' are drawn at right angles to the tangent at then and Y' are on the circum- ference of the auxiliary circle and SY S'Y' BC2 29 If circle be described touching the axis major in one focus and passing through one end of the axi3 minor AC will be mean proportional between BC and the diameter of this circle 30 The area of the ellipse is to the area of the auxiliary circle as ΒC to AC

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