Calendar: 1872-1873 Page 531

532 GENERAL LITERATURE AND SCIENCE Determine the focus and directrix of parabola which shall touch two given straight lines at given points 10 If two diameters of conic be such that one of them bisects all chords parallel to the other then the second will bisect all chords parallel to the first 11 Determine the equation of chord of conic section in ttrins of polar coordinates Deduce the polar equation to the tangent 12 Investigate the equation to the hyberbola referred to its asymptotes 13 The perpendiculars let fall from the point of intersection of two tangents at the extremities of any two diameters of an ellipse upon those diameters are inversely proportional to the lengths of the diameters upon which they fall 14 Show that the asymtotes real or imaginary of the conic ax 2hxy bf 2ffx 2ey are parallel to the lines ax 2hxy bf Find the equation to the axes of the conic and the coordinates of the foci 15 The three diagonals of any quadrilateral circumscribing conic form self conjugate triangle with respect to the conic 16 If the vertices of two parabolas whose axes are at right angles coincide the polar reciprocal of one of them with respect to the other is rectangular hyperbola III tomttro From given point to draw straight line equal to given straight line The angles at the base of an isosceles triangle are equal to each other and if the equal sides be produced the angles on the other side of the base shall be equal If the same straight line bisects the base and the vertical angle the triangle is isosceles Any two sides of triangle are together greater than the third side