Calendar: 1881-1882 Page 679

680 SCIENCE FREAKE SAMBROOKE Inscribe an equilateral and equiangular pentagon in given circle If straight line be drawn parallel to one of the sides of triangle it shall cut the other sides or those sides pro- duced proportionally and conversely if the sides or the sides produced be cut proportionally the straight line which joins the points of section shall be parallel to the remaining side of the triangle Find three points one on each side of triangle such that when they are joined the triangle shall be divided into four equal triangles Define conic section On given base AB any isosceles triangle PAB is described On AP another triangle QAP is described similar to PAB Find the locus of Define the circle of curvature יי and show that the chord of the circle of curvature at the point Ρ of parabola drawn parallel to the axis ASP If SY and SY' be the perpendiculars from the foci upon the tangent to an ellipse at any point and Y' are on the circumference of the auxiliary circle If the directrices intersect the axis major produced in and X' then XY' and ΧΎ' are equally inclined to the axis major 10 Define the asymptotes of hyperbola and show that the tangent and normal at any point of hyperbola meet the asymptotes and axes respectively in four points which lie on circle passing through the centre of the hyperbola 11 Find the equation to straight line in the form mx c9 and draw the straight lines represented by the equations 3x θ 12 Find the length of the perpendicular from the point on the line 13 On the line joining he points and as diameter circle is described find its equation 14 Find the polar equation to an ellipse the focus being the pole