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a2 sin2 abscissa asymptotes axes axis of x centre chord of contact circle conjugate diameters conjugate hyperbola constant corresponding cos2 denote determined directrix distance ellipse equa equal excentricity expression 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 length Let the equation line be drawn line drawn line joining lines meet lines represented lines which pass major axis meet the curve middle point negative normal oblique obtain ordinate parabola parallelogram Pascal's Theorem perpendicular point h point of intersection polar co-ordinates polar equation pole positive preceding article proposition prove radical axis ratio rectangular required equation respectively right angles shew shewn sides Similarly straight line passing suppose tangents are drawn tion touch trapezium triangle vertex
Pàgina 327 - PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples.
Pàgina 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Pàgina 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.
Pàgina 127 - A diameter of a curve is the locus of the middle points of a series of parallel chords.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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).