Calendar: 1852-1853 Page 337

APPLIED SCIENCES 333 Draw tangent to an ellipse and show if it be drawn to the extremity of the latus rectum and through any point Ρ in the ellipse an ordinate NPQ be drawn meeting the tangent in SP NQ If ax be the equation to line passing through the intersection of χ -j- and χ find OC Λ Find χ when is maximum a2 x'z Integrate the following differentials x4 χ adx dx ן- a2 s-2 bsin tan י And sm cx 2dx Ζι χ3 dx xdx x5 x4 right angle Β CP is moved so that Ρ and are always on two axes at right angles to each other find the locus of Ρ and if BC CP show that the area traced by Ρ π CP2 Expand -f s'm according to the powers of 10 Prove -- being the area of curve deduce from it the equation -j 11 At point of contrary flexure Ex 92 12 Any number of rectangles being inscribed in triangle find the locus of their centres 13 Show that there is cusp at the origin of the curve defined by χ y2 x2 x4 14 hemispheroid and paraboloid have the same base and altitude compare their volumes