Calendar: 1875-1876 Page 588

584 GENERAL LITERATURE AND SCIENCE 19 The two tangents to parabola from an external point subtend equal angles at the focus 20 Two straight lines are drawn from the vertex of parabola at right angles to each other the points where these straight lines meet the curve are joined thus forming right angled triangle find the least area of this triangle 21 Find the equation to the tangent at any point of an ellipse Determine point in the ellipse such that the tangent there is equally inclined to the axes 22 The normal at any point of an ellipse bisects the angle between tbe focal distances of that point 23 Two ellipses have common centre and their axes coi cide in direction also the sum of the squares ot the axes is the same in both ellipses find the equation to common tangent 21 Find the equation to the ellipse referred to pair of con- jugate diameters as axes If straight lines drawn through any point of an ellipse to the extremities of any diameter meet the conjugate CD in points prove that CM CN CD2 25 PQ is chord of an allipse at right angles to the major axis A' PA QA' are produced to meet at £ shew tha the locus of is an hyperbola having the same axes as the ellipse 26 Find the equation to the hyperbola referred to the asymp- totes as axes Shew also that the portion of the tangent at any point intercepted between the asymptotes is bisected at the point of contact IX --CngltiSl iiStorp What were the difficulties in the way of James 's acces- sion to the crown of Englai and how were they overcome What were the arguments in favour of the union of the two crowns and what were the objections urged against it both by Englishmen and by Scotchmen Give brief account of the Hampton Court Conference By whose advice was James mainly governed until 1612 Give short account of this minister and of the king's favour- ites who succeeded