Calendar: 1880-1881 Page 644

644 GENERAL LITERATURE AND SCIENCE 12 PSp is focal chord of parabola RDr the directrix meeting the axis in and any point on the curve Prove that if QP Qp be produced to meet the directrix in half the latus rectum is mean proportional between DR Dr 13 If PN be an ordinate to the parabola at the point Ρ then PN 4AS AN If PL be drawn at right angles to AP meeting the axis in Ly and PN be the ordinate of then NL AS 14 If QF be an ordinate to the diameter PF then QV2 4SP PV 15 If the tangent to the ellipse at Ρ meet the axis major produced in and PN be the ordinate of the point then CT CN CA 16 If Ρ Τ be tangent to an ellipse meeting the axis in and AP A'P be produced to meet the perpen- dicular to the major axis through Τ in and Qthen QT Q'T 17 To draw pair of tangents to an ellipse from an external point 18 Find the locus of the intersection of pair of tangents at right angles to each other 19 Draw the straight lines χ 2x χ and find the area of the triangle formed by them λ' "'' ''ίίΫ "7llf iA 20 Find the condition in order that three straight lines may meet at point Show that the straight lines drawn from the angles of triangle perpendicular to the opposite sides meet at point ד tf als 21 circle passes through the points and show that its centre lies on the line χ 22 Find the polar equation to circle and determine what is represented by the equation rz י racos 2Θ sec θ 2a2 23 Find the equation to the normal at any point of parabola and show that from any point there cannot be drawn more than three normals to parabola