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abscissa algebraic angle anharmonic ratio axes axis axis of X becomes called centre chord circle co-ordinates coefficients common completely condition conic conjugate considered constant contained corresponding curve cuts defined definition determine diameter direction distance divide draw drawn ellipse equal example EXERCISES expression Find the equation fixed point focus four points geometry given gives Hence hyperbola identity imaginary intercepts length line joining line passing locus meet middle point negative normal opposite origin pair parabola parallel passing pencil perpendicular plane point of intersection polar pole position preceding problem projection Proof quantities radical radii radius rectangular reduced referred relation Remark represent respectively satisfy segments Show sides signs square straight line Substituting suppose surface tangent Theorem third tion triangle values vertices whence Write
Página 99 - 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.
Página 61 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.
Página 13 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Página 225 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Página 159 - 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.
Página 61 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.
Página 57 - ... 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
Página 90 - The locus of the point of intersection of two tangents to a parabola which...