Plane Analytic Geometry: With Introductory Chapters on the Differential Calculus |
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Common terms and phrases
analytic geometry asymptotes Ax₁ Ax² axis of x B₁ B₁y B₂y barycenter bisectors By₁ C₁ called chord circle conic conjugate diameters conjugate hyperbola Consequently constant coördinate axes degree determine diagonals direction directrix distance ellipse equa equal EXERCISES Find Figure Find the coördinates Find the equation Find the locus fixed points foci focus formula Hence Hesse's Normal Form intercepts latus rectum length line joining line parallel M₁ meet method middle points moving point negative oblique coördinates origin P₁ P₁P₂ P₂ parabola perpendicular Plot point halfway point of inflection point of intersection point x1 polar coördinates PROBLEMS TO CHAPTER Proj projections Prove quadrant quantity radius rectangle rectangular coördinates right angles segment slope solving square standard form straight line system of coördinates tangent theorem tion transverse axis triangle whose vertices variables vertex x₁ y₁
Popular passages
Page 96 - Find the locus of a point, the distances of which from two given straight lines have a fixed ratio. 143. Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third.
Page 97 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 17 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Page 17 - 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 109 - An ellipse is a curve which is the locus of a point that moves in a plane so that the sum of its distances from two fixed points in the plane is constant.
Page 109 - An hyperbola is a curve which is the locus of a point that moves in a plane so that the difference of its distances from two fixed points in the plane is constant.
Page 96 - 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 109 - It may also be defined as the locus of a point which moves in a plane so that its distance from a fixed point, called the focus.
Page 15 - The straight lines joining the vertices of a triangle to the middle points of the opposite sides meet in a point* which is for each line the point of trisection further from the vertex.
Page 107 - The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle.