Elements of analytic geometry |
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a²b³ abscissa algebraic Analytic Geometry anharmonic ratio axes of co-ordinates axis of X bisects called centre of similitude circle co-ordinate axes co-ordinate planes coefficients condition conic section conjugate diameters conjugate hyperbola constant cosines curve direction-cosines direction-vectors directrix distance distance-ratios drawn ellipse equa equal expression Find the equation Find the locus fixed point focus four points geometry Hence imaginary infinity intercepts junction-point latus rectum length line intersects line joining line passing locus middle point negative normal ordinate origin parabola parallel pencil perpendicular points of intersection polar polar equation pole position PROBLEM Proof quadric quantities radical axis radius rectangular represent respectively second degree segments Show sides sine-ratio straight line Substituting subtangent suppose tangent THEOREM three points tion triangle values vertex vertices whence Write the equation x₁ y₁
Popular passages
Page 115 - 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 151 - THE simplest property of the hyperbola is that it is the locus of a point the difference of whose distances from two fixed points is constant. The two fixed points are called tho foci.
Page 69 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.
Page 15 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Page 234 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 175 - For example, the locus of a point which moves in such a way that its distance from a fixed point is always equal to its distance from a fixed straight line, is a parabola.
Page 69 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.
Page 63 - ... the tangent of the angle which the line makes with the axis of abscissae), was lately employed by M. Crova* for the discussion of experiments relating to the degree of constancy possessed by so-called
Page 106 - The locus of the point of intersection of two tangents to a parabola which...
Page 17 - Let x, y be the co-ordinates of any point P referred to the...