Calendar: 1874-1875 Page 554

r 54 GENERAL LITERATURE AND SCIENCE Show that the tangent to conic makes equal angles with the focal distances of the point of contact parabola is described with its locus at one focus of given Conic and touches the conic prove that its directrix will touch fixed circle Find the equation to the tangent to parabola in terms of the angle which it makes with the axis Hence determine the locus of the intersection of two tangents at right angles to each other Find the equation to the locus of the middle points of system of parallel chords in hyperbola referred to its asymptotes Parabolas are described touching two lines at right angles to each other show that if the chords through the points of con- tac are parallel to one another the locus of the vertices of the parabolas is straight line Find the polar equation to the ellipse one of the foci being the pole and the prime radius passing through the nearer vertex Show that the equation g' cos -f cos referred to the same origin represents straight line which has only one point in common with the curve Find the equation to the line joining the points of contact of tangents drawn from any given point to an ellipse If from any point in the exterior of two similar and similarly situated ellipses tangents be drawn to the interior ellipse the ordinate of that point will bear constant ratio to the projection of the chord of contact on the axis major of the ellipse Define the eccentric angle of any point on an ellipse and obtain the equation of the normal to an ellipse in the form cos θ 811 If the normals at three points whose eccentric angles are α β γ meet in point then will β η cl -4- β tan----- cota tani--- cot tan- coly Prove that the equation