Calendar: 1885-1886 Page 678

670 GENERAL LITERATURE AND SCIENCE Find the equation to the circle referred to any oblique axes What does the equation become when the axes are two tangents inclined at an angle of 60 Find the locus of point which is such that tangents from it to two concentric circles are inversely as their radii Find the value of that the circles -a 2- c2 and x- c2 may touch each other Find the polar equation to the parabola when the vertex is the pole 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 10 Circles are described on any two foral chords of para- bola as diameters Prove that their common chord passes through the vertex of the parabola 11 Find the equation to the tangent at any point of an ellipse Find point on the ellipse such that the tangent there is equally inclined to the axes 12 Normals at and the ends of semi-conjugate dia- meters meet at find the equation to QC and shew that QC is perpendicular to PD FIRST YEAR If two straight lines cut one another the vertical or opposite angles shall be equal If the same straight line bisects the base and vertical angle of triangle the triangle is isosceles Any two sides of triangle are together greater than the third side In given indefinite straight line find point such that the sum of its distances from two given points on the same side of the straight line shall be the least possible