Calendar: 1860-1861 Page 481

482 GENERAL LITERATURE AND SCIENCE 10 If the normal at passes through the extremity of the axis minor what is the excentricity of the ellipse 11 The area of the parallelogram which touches the ellipse at the ends of conjugate diameter is constant 12 Find the equation to the hyperbola referred to the asymp- totes as axis י II -problems Show that the sum of the cubes of the roots of the equation η η-1 2-מ η χ -px qx rx τ is 3pq- Sr -ρ3 Give Des Cartes' method for the solution of biquadratic and by it find the roots of xi 8x If 4x3 16x 16 has equal roots find all the roots Find the equations to the straight lines joining the centre of the circle x2 y2 4a2 with the points in which the line χ meets it Ρ Op is diameter of an ellipse the middle point of chord parallel to this diameter Ρ intersects in show that the locus of Λ is parabola Of all the parabolas which can be inscribed in circle touching the circle at the vertex the greatest area cut off by the chord common to the parabola and circle is that for which the chord bisects the radius of the circle Find the area included by the curves 4a2 ys β χ ay Ify ax3 2ayx2 be theequation to acurve there 128 is node whose area 777 a2 100 Find the locus of the intersections of the normals at any two points of parabola on opposite sides of its axis the ordi- nates of which are as parabolic area revolves round its extreme ordinate find the volume and surface of the solid generated