Calendar: 1880-1881 Page 634

634 GENERAL LITERATURE AND SCIENCE Show that the locus of point is straight line when it moves so that the sum of the three angles which the three normals drawn from it to the parabola make with the axis is constant The locus of the focus of parabola of latus rectum 40 which touches the axis of χ at the origin has for its equation Find the equation of the bisectors of the angle between the lines aafi 2hxy -f by 10 QQ' is chord of parabola touching confocal and coaxial parabola show that QQ' varies as the parameter of the diameter bisecting it 11 Prove that if ax 2hxy bp 2gx 2fy be the equation to conic then 271 cos ω ab h2 --9-ל and sm Δω sin Jco are the same however the axes may be changed where ω is the angle between the axes Find the axes of the conic x2 Sxy y2 the axes being rectangular 12 Find the equation to the two tangents from an external point to the conic given by ax2 2hxy by2 Hence find the locus of the intersection of two tangents at right angles to one another 13 What is the excentric angle of any point on an ellipse Find the equation to the chord joining two points whose excentric angles are αβ 14 Find the equation to conic having double contact with the conic at the point where the line touches it If two conies have each double contact with third their chord of contact with the third conic and pair of their chords of intersection with each other will all pass through the same point What does this become when the third conic is pair of straight lines and the other two are intersecting circles