Calendar: 1850-1851 Page 326

322 APFLIED SCIENCES Prove that ο ι Λ Κ 0י and find its value when θ Find the evolute of the ellipse and its area Show that ff χ -ffe dr Θ if χ cos and sin Find the equation to the normal at any point of the parabola in terms of its inclination to the axis of Thence find the locus of the intersections of pairs of normals which include an angle 90 Given the base and vertical angle of triangle find the locus of the centre of the inscribed circle 10 Determine the length of an arc of the Lemniscata 11 Trace the curve defined by x3 -f- x2 and find its area 12 Find the equation to the cycloid and the solid generated by revolution round its asymptote VI If -f χ sin tan find in terms of If be the length of curve defined by then dJ- Λ λ dy dx co-ordinates ds λ r4 -- and deduce from it the formula for polar xz Find the length of the semicubical parabola Find the equation to the spiral of Archimedes and its length If Ρ be drawn parallel to Λ the base of the triangle ABC and Β Ρ be joined intersecting in find the locus of as Ρ moves from Β towards dUU χ If 11 χ β prove strictly that -- זן η