Elements of Analytic Geometry |
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Common terms and phrases
a² b2 a²b² abscissa asymptotes auxiliary circle axes of coördinates axis of x bisects all chords called centre chord of contact chords parallel 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 polar fixed point focal chord focal radii foci given point Hence intercepts intersection latus rectum Let the equation line parallel loci meet middle point negative obtain ordinate origin parabola y²=4px perpendicular point h point of contact point x1 polar coördinates polar equation positive Prove quadrant radical axis rectangular represent respect right line secant semi-minor axis slope subnormal substituting subtangent system of coördinates tangents drawn touch the circle Transform the equation triangle values vertex Whence x₁ 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 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.
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 138 - 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 88 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.
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 89 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.