Calendar: 1879-1880 Page 603

GENERAL LITERATURE AND SCIENCE 603 14 What relation must hold among the constants that the equation ax1 bxy cy2 dx ey -f0 may represent two straight lines 15 point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant show that the locus of the point is circle 16 Find the equation to the tangent at any point of circle and show that from any external point two tangents can be drawn to circle 17 If the tangent to parabola at any point Ρ intersect the directrix in then SZ will be at right angles to SP 18 If PN be an ordinate to parabola at the point then PJVJ 4AS AN And if PL be drawn at right angles to AP meeting the axis in then NL AAS 19 Draw pair of tangents to parabola from an external point 20 If QVbe an ordinate to the diameter PV then QV2 ASP PV 21 If from point Ρ of circle PG be drawn to the centre and be the middle point of the chord PQ drawn parallel to fixed diameter ACB then the curve traced out by the inter- section of CP and AR is parabola 22 PQ is chord of parabola PT the tangent at straight line parallel to the axis of the parabola cuts the tangent at the arc PQ at and the chord PQ at Prove TE ER PR RQ 23 Trace the curve χ χ2 and determine whether the straight line χ is tangent to it 24 Find the equation to parabola referred to tangents at the ends of the latus rectum as axes 25 Find the equation to the normal at any point of an ellipse and show that the normal at any point bisects the angle between the focal distances of that point 26 Find the locus of point such that the two tangents from it to an ellipse are at right angles 27 Given the coordinates of one end of diameter of an ellipse to find those of both ends of the conjugate diameter