Calendar: 1886-1887 Page 681

GENERAL LITERATURE AND SCIENCE 683 intersect at right angles its diameter xy the segments of the chord c1 prove that x2 y2 d2 f- c22 12 Find the equation to the tangent at the point of the parabola whose equation is y2 Aax What must be the values of and so that the perpen- flicular from the focus on the tangent at may be equal to the latus rectum 13 Prove that the latus rectum of an ellipse is third proportional to the major and minor axes and find the latus rectum and area of the ellipse whose equation is 25y2 16a2 WOx 14 The line Ix my intersects the hyperbola a2y2 b2x2 α2δ2 form the equation to the lines through the origin and points of intersection Deduce the relation that must hold in order that the given line may touch the hyperbola IV -Crtgononutn &c Determine an expression for all angles having the same sine as given angle Solve the equation sin θ sin 3Θ Define logarithm and prove that log&0 ogab Given log102 3010300 determine log10625 log10l£ log12 610 sin 45 log10l28 log10l25 and from the last two calculate approximately log10l26 and logiol'27 Α9 are three points 100 ft distant from one another is another point outside the triangle and between the sides Β BC The angles subtended by AO at Β and are observed to be 15 and 30 respectively determine to two places of decimals the distance of from If Δ is the area of triangle ABC ra rc the radii of the escribed circles the radius of the circumscribed circle Pa pb Pc the perpendiculars from the angular points upon the opposite sides prove that cos cos Β cos cos sin Β sin cos Β sin sin co3 sin sin