Calendar: 1860-1861 Page 480

GENERAL LITERATURE AND SCIENCE 481 15 string whose length is 10 yards is unwound from circular post whose circumference is yard Find the length of the path described by the extremity of the string MATHEMATICS -MIDDLE SCHOLARSHIP -Conic Sections Find the equation to the straight line which passes through the origin and through the intersection of the straight lines whose equations are m1 χ city m2 χ-f-f2 Also determine the relation between these constants when the required line bisects the angle between the given lines Find the general equation to the circle referred to rect- angular coordinates What form does the equation take when the circle touches the axis of χ and line drawn through the origin at an angle of 45 with the axis of xt Taking the centre of the circle as the origin of coordinates find the coordinates to that point the tangent to which makes an angle with the axis of which is double of that which it makes with the axis oiy Find the equation to the tangent to the parabola Reduce it for the point whose abscissa is four times as far from the vertex as the focus is Find the equation to the parabola the axis being any diameter and the tangent at the point where the diameter meets the curve Show that the circle described on SP as diameter touches the tangent at the vertex of the parabola Define the ellipse and thence deduce its equation the centre being the origin of coordinates and the axis of the curve the axis of coordinates Find the polar equation to the ellipse the focus being the pole also find β when SP CB Find the equation to the normal to the ellipse and show that it bisects the angle between the focal distances to the point of contact Η Η