The Elements of Plane Analytic Geometry: A Text-book Including Numerous Examples and Applications, and Especially Designed for Beginners[J.] Wiley, 1887 |
Common terms and phrases
A₁ a² b2 abscissa algebraic Analytic Geometry arbitrary constants asymptotes axes b₁ b2 a² bisects all chords bola centre circle x² conic sections conjugate diameters conjugate hyperbolas coördinates cos² curve directrix distance drawn ellipse equa equal equations of tangent expresses extremities figure Find the equations find the locus fixed point focal radii foci focus formulas Geometry given line given point initial line intercept on O Y last example latus rectum Let us find line which joins M₁ major axis middle points negative ordinate origin P₂ parabola parallel to OX perpendicular plane point P₁ points of intersection polar equation positive Prove quantities radius ratio rectangle represent required equation secant semi-major axis sin² slope square straight line tangent and normal theorem tion triangle Trigonometry vertex x₁ X₂ y₁ λ₁ λε
Popular passages
Page 70 - A parabola is a curve which, is the locus of a point that moves in a plane so that its distance from a fixed point in the plane is always equal to its distance from a fixed line in the plane.
Page 151 - ... (17.) By means of this equation, prove that the locus of the middle points of chords of an ellipse, which pass through the left-hand extremity of the major axis, is another ellipse. What are its axes, and how is it situated ? (18.) Prove that if the right-hand focus of an ellipse is the origin (the major axis being the axis of x), the radius connecting that focus with any point of the ellipse equals a (i...
Page 97 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.
Page 74 - ... any chord of the larger drawn from the point of contact is bisected by the circumference of the smaller.
Page 104 - To find the locus of the middle points of chords of a circle, which pass through a given point. Let the given point be the pole, and the line joining it with the centre be the initial line. Let P ' P" be any chord which passes through 0,and let /"be its middle point, with coordinates r and &.
Page 106 - CP = D'M'. In the same way all the points may be constructed. III. An ellipse, which may be generated by a point moving in the same plane, so that the sum of its distances from two fixed points shall be constantly equal to a given right line.
Page 11 - In any right triangle, the straight line drawn from the vertex of the right angle to the middle of the hypotenuse is equal to one-half the hypotenuse (I.
Page 106 - F'. These points will be the foci, for DF + DF' = 2CV = VV. IV. The hyperbola, which may be generated by moving a point in the same plane, so that the difference of its distances from two fixed points shall be equal to a given line. The two fixed points are the foci.
Page 102 - Find the locus of the center of a circle which has a given radius and passes through a given point.
Page 105 - Find the locus of the middle points of chords drawn from the extremity of any diameter of a circle.