Calendar: 1877-1878 Page 593

GENERAL LITERATURE AND SCIENCE 591 XIX tomcirj airtf Snalgttcal comctrj The base of triangle the vertical angle and the difference of the sides are given construct the triangle If perpendiculars he let fall from point on the three sides of triangle and if the triangle formed by joining their feet be similar to the original triangle prove that the point is the centre of the circumscribed circle Draw pair of tangents to parabola from an external point lfPQ be the chord of contact prove that the centre of the circle about OPQ lies in the straight line drawn from the focus jS' at right angles to SO Two of the normals drawn to parabola from point Ρ make equal angles with given straight line Prove that the locus of Ρ is parabola If QQ' be chord parallel to one of the equal conjugate diameters of an ellipse whose centre is prove that CQ2 CQ'2 is constant pair of conjugate diameters of an ellipse intersect 011 tangent at either vertex length which subtends complementary angles at the foci Ρ is point on an ellipse whose foci are and and r' the radii of the circles escribed to HPS opposite the angles Η and Prove that where is the ordinate of Obtain the condition that the general equation of the second degree may represent parabola and find the equation to its axis If in the equation ax2 2hxy by2 yx the axes he altered without changing the origin then ab A2 4- 1cos& -- and -י--- smza sin-ω remain unaltered where ω is the angle between the axes