Elements of Analytic GeometryGinn, 1886 |
Contents
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Common terms and phrases
a² b2 abscissa asymptotes auxiliary circle axis of x called centre chord of contact chord passing circle x² coincide conjugate diameters conjugate hyperbola constant curve denote directrix draw ellipse equal equilateral hyperbola Find the distance Find the equation Find the length Find the locus Find the points Find the polar fixed point focal chord focal radii foci focus Hence intercepts intersection latus rectum Let the equation line parallel loci meet middle point MP=y negative obtain ordinate origin parabola y² parabola y²=4px perpendicular plane point h point of contact point x1 polar axis polar coördinates polar equation positive Prove quadrant radical axis represent respect right line secant semi-minor axis slope subnormal substituting subtangent system of coördinates tangents drawn touch the axis touch the circle Transform the equation triangle values vertex Whence y=mx+b y₁ zero
Popular passages
Page 33 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.
Page 190 - 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 113 - Parabola is the locus of a point whose distance from a fixed point is always equal to its distance from a fixed straight line.
Page 136 - An ellipse is the locus of a point, the sum of whose distances from two fixed points is constant. In Fig. 10.12, the two fixed points are labeled F and F' and are termed the foci of the ellipse, with x coordinates /and/+ 2c.
Page 234 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a figure upon a plane is the locus of the projections of all the points of the figure upon the plane. Thus, A'B' represents the projection of AB upon plane MN.
Page 205 - These three curves are all loci of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line.
Page 163 - Arts. 14, 5, and 20 it has been shown that the ellipse, the parabola, and the hyperbola are each the locus of a point, which moves so that its distances from a fixed point (/<>««*) and a fixed line (directrix) are in a constant ratio (eccentricity).
Page 88 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.
Page 89 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 59 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.