Elements of Analytic Geometry |
Other editions - View all
Common terms and phrases
a² b2 a²b² abscissa asymptotes auxiliary circle axis of x called centre chord of contact chords parallel circle x² coincide conjugate diameters conjugate hyperbola constant curve denote directrix ellipse equal equilateral hyperbola Find the distance Find the equation Find the length find the locus Find the points fixed point focal chord focal radius foci focus given point Hence intercepts intersection latus rectum Let the equation line parallel loci major axis meet middle point negative obtain ordinate origin P₁ parabola y² parabola y²=4px perpendicular plane point h point of contact point x1 polar coördinates polar equation pole h positive Prove radical axis radii respect secant semi-minor axis slope subnormal subtangent system of coördinates TANGENTS AND NORMALS tangents drawn touch the circle Transform the equation triangle values vertex Whence x₁ y=mx+b y₁
Popular passages
Page 21 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.
Page 172 - 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 45 - 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 99 - 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 122 - 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 11 - REVISED. BY GEORGE A. WENTWORTH. Wentworth's Plane and Solid Geometry. Revised. 473 pages. Illustrated. For introduction, $1.25. Wentworth's Plane Geometry. Revised. 256 pages. Illustrated. For introduction, 75 cents. Wentworth's Solid Geometry. Revised. 229 pages. Illustrated. For introduction, 75 cents. THE history of Wentworth's Geometry is a study in evolution. It was the corner stone on which was built a now famous...
Page 187 - 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 149 - 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 75 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 36 - ... lines, and the perpendiculars from the three vertices of the triangle upon this line will be equal, by Chap. I, II, 13. A perpendicular to AB erected midway between any two of these three is perpendicular to the corresponding side of the triangle at its middle point (Chap.