Calendar: 1876-1877 Page 580

580 GENERAL LITERATURE AND SCIENCE What points on the axis of χ are at perpendicular distance from the straight line -Y The straight lines drawn from the angles of triangle to the middle points of the opposite sides meet at point Find the equation to circle of radius referred to two tangents inclined at an angle ω as axes Find the equation to the tangent at any point of circle Find the condition that Ax -f By touch the circle af by In the parabola the latus rectum BC AS Shew that the diameter of the circle described about the triangle BAC is equal to AS If the tangent at any point Ρ of parabola meet the axis produced in the point and PN he the ordinate of the point then NT AN If circle be described about the triangle SPN the tangent to it from PN 10 If PNhezn ordinate to the parabola at the point then PN2 AS AN AB and AC are two lines at right angles to each other From fixed point on AC CR is drawn parallel to AB On AR produced if necessary Ρ is taken such that the perpendicular PN upon AB is equal to CB Prove that the curve traced out by Ρ is parabola 11 If the tangent at any point Ρ intersect the tangent at the vertex in then SY will bisect PT at right angles and will be mean proportional between SA and SP If the tangent cut the directrix in then PT YZ AS SP 12 If from point Ο pair of tangents OQ and OU be drawn to parabola the triangles OSQ OSQ will be similar and OS will be mean proportional between SQ and £ If two equal tangents be cut by third tangent their alternate segments are equal 13 If QP be an ordinate to the diameter PV then QF 4SP PF If QD be drawn at right angles to PF then QB2 4AS PF