Notes on Analytical Geometry: An Appendix

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Clarendon Press, 1903 - 171 páginas
 

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Página 30 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Página 144 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Página 7 - WALL. A Concise French Grammar, including Phonology, Accidence, and Syntax, with Historical Notes. For Use in Upper and Middle Forms. By ARTHUR H. WALL, MA Crown 8vo, 4*.
Página 89 - Show that the area of the triangle formed by the asymptotes and any tangent to a hyperbola is constant.
Página 66 - If the sum of the eccentric angles of two points on an ellipse is constant and equal to 2a, the chord joining those points is always parallel to the tangent at the point whose eccentric angle is a.
Página 150 - ... constant. 3. Prove that the four vertices of a parallelogram circumscribing an ellipse and its two foci are on the same equilateral hyperbola. 4. Given an ellipse and a circle concentric with each other, the radius of the circle being equal to the sum of half the major axis and half the minor axis of the ellipse. Prove that the locus of the point of intersection of the two normals to the ellipse at the points at which two tangents are drawn to the ellipse from any point on the circle is a circle....
Página 85 - If two circles are tangent to each other, any straight line drawn through their point of contact subtends arcs of the same number of degrees on their circumferences. (§ 197.) (Let the pupil draw the figure for the case when the ® are tangent internally.) 60.
Página 17 - To find the direction and magnitude of the axes of the conic represented by the general equation of the second degree.

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