A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 páginas |
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A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and ... Isaac Todhunter Visualização completa - 1862 |
Termos e frases comuns
a² sin² a²b² a²b³ a²y abscissa asymptotes ax² axes axis of x b² cos² b²x² centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant cy² denote directrix distance ellipse equa equal external point find the equation find the locus fixed point focal chord focus given lines given point given straight line Hence the equation inclined latus rectum Let the equation line drawn line joining lines meet lines represented lines which pass major axis meet the curve middle point negative normal ordinate origin parabola parallel parallelogram perpendicular point h point of intersection polar co-ordinates polar equation pole positive preceding article radical axis radius ratio rectangular required equation respectively right angles shew shewn sides Similarly suppose tangent triangle vertex x₁ y₁
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Página 141 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Página 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Página 25 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Página 127 - A diameter of a curve is the locus of the middle points of a series of parallel chords.
Página 10 - Find the area of the triangle formed by joining the first three points in question 1. 5. A is a point on the axis of x and B a point on the axis of y ; express the co-ordinates of the middle point of AB in terms of the abscissa of A and the ordinate of B ; shew also that the distance of this point from the origin = ^ AB.
Página 268 - Two conic sections have a common focus 8 through which any radius vector is drawn meeting the curves in P, Q, respectively. Prove that the locus of the point of intersection of the tangents at P, Q, is a straight line.
Página 20 - To find the equation to a straight line in terms of the perpendicular from the origin, and the inclinations of the perpendicular to the axes.
Página 300 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Página 50 - ... proves the proposition. The lines drawn from the angles of a triangle perpendicular to the opposite sides meet in a point. The equation to BC is, (Art. 35), hence the equation to the line through A perpendicular to BC is, (Art. 44), y The equation to AC is ... (4).