Elements of Analytical Geometry |
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Common terms and phrases
a²+b² abscissa approximation asymptote ax²+2hxy+by²+2gx+2fy+c=0 ax²+2hxy+by²=0 bisectors bisects circle whose centre coincident points conic constant diameter directrix distance draw the graph drawn ellipse equal example EXERCISES find the coordinates Find the equation fixed circle fixed point focus following equations freedom equations given gradient harmonic pencil harmonic range harmonically conjugate Hence hyperbola infinity latus rectum lies line ax+by+c=0 line joining locus m₁ m₂ meets the curve middle point negative ordinate origin pair parabola parallel passes perpendicular point of contact point of inflexion point of intersection point P moves polar positive direction Prove radical axis radius rectangular axes respectively right angle roots scale unit secant simultaneous equations sketch the locus specified square straight line tangent THEOREM triangle variable circle variable point velocity vertex vertices x-axis X'OX x=a+bt x₁ x²+y²+2gx+2fy+c=0 y-axis Y'OY y=c+dt y=mx+c y₁ zero
Popular passages
Page 465 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Page 350 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 171 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 452 - If two conies have each double contact with a third, their chords of contact with the third conic, and a pair of their chords of intersection with each other, will all pass through the same point, and will form an harmonic pencil.
Page 268 - Radius = - m. 2я + 9 4я+18 271 + 9 14. A piece of the wire of length 10 ms, is to be cut into two pieces, one of which is to be bent into the form of a square and the other into the form of a circle. Find when the sum of the areas of the circle and the square is minimum.
Page 424 - If, through a given point on a conic, any two straight lines at right angles to. each other be drawn to meet the curve, the straight line joining their extremities will pass through a fixed point on the normal of the given point.
Page 325 - That is : the sum of the focal distances of any point on an ellipse is constant and equal to the major axis.
Page 140 - B respectively to the opposite sides produ'ced: prove that the square on AB is equal to the sum of the rectangles contained by BC, BD and AC, AE.
Page 452 - ... 5. If three conies have each a double contact with a fourth, six of their chords of intersection will pass, three by three, through the same points. 6. ABC is a triangle, and P any point, such that the squares of the three areas...
Page 449 - The focal chord of curvature at any point of a conic is equal to the focal chord of the conic parallel to the tangent at that point. » Let PSF be any focal chord of a conic, PT the tangent at P, and RSR' the focal chord parallel to PT.