Calendar: 1876-1877 Page 589

GENERAL LITERATURE AND SCIENCE 589 XIX romctn airtl Hnalpttcal comctrj Given the base vertical angle and sum of the sides con- struct the triangle Prove that the shortest distance between two straight lines is perpendicular to each The chord of the circle of curvature at point Ρ of para- bola parallel to the axis 4SP If the chord of contact of two tangents to parabola be normal at one end the tangent at the other is bisected by the perpendicular through the focus on the line joining the focus to the point of intersection of the tangent Find the polar reciprocal of one circle with respect to another and determine the positions of its focus and directrix Determine the length of the chord of the ellipse £ ι י a2 b2 whose equation is α י 2' is focus and the centre of an ellipse and Ρ any point upon it Prove that the locus of the intersection of the diameter conjugate to CP with the line through at right angles to SP is the curve a2 x2 y2 x2 at Find the locus of the foci of parabolas which pass through two given points and have their axes in given direction Three normals are drawn to central conic from any point in the curve prove that their product is equal to 2a2b2 a2 where ρ is the radius of curvature at the point 10 If the equation to conic referred to oblique axes inclined at an angle is ax bf 2cr$ then the equation to its axes is χ2 f2 xy cos ω ax2 bf 11 chord PQ of an ellipse is normal at Ρ and is its pole