...parallel to the axis of x or to the axis of y, according as A is less than, or greater than, B. 162. To find the locus of a point which moves so that the ratio of its distances from a fixed point and a fixed straight line is constant and less than unity. Let e denote the constant ratio, 2p the distance...

...equal to the eccena tricity of the ellipse as defined in § 128. Whence an ellipse is often defined as The locus of a point which moves so that the ratio of its distances from a fixed point and a fixed straight line is constant and less than unity. Fis called the Pocus ; DN, (he Directrix. The...

...HYPERBOLA Special Equation of the Second Degree Ao? — By* 115. The hyperbola defined. An hyperbola is the locus of a point which moves so that the ratio of its distance from a fixed point, called the focus, to its distance from a fixed line, called the directrix,...

...from a certain point •within the circle to the boundary is constant. A circle may also be defined as the locus of a point which moves so that the ratio of its distances from two fixed points is constant. This proposition has been proved as prop. 4 of the Theorems and Examples...

...sides of a trapezium divides the other two sides (or those sides produced) proportionally. Ex. 18O2. Find the locus of a point which moves so that the ratio of its distances from two intersecting straight lines is constant. Ex. 18O3. Through a given point within a given angle draw...

...the major axis, and the perpendicular bisector of this diameter the minor axis. It is also defined as the locus of a point which moves so that the ratio of its distance from a fixed point, called the focus, to its distance from a fixed line (DD'), called the...

...the major axis, and the perpendicular bisector of this diameter the minor axis. It is also defined as the locus of a point which moves so that the ratio of its distance from a fixed point, called the focus, to its distance from a fixed line (DD'), called the...

...will be given. To investigate the form of the curve use. may be made of the definition: the ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point (the /of«) to its distance from a straight line (the directrix) is constant...

...will be given. To investigate the form of the curve use may be made of the definition: the ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point (the focus) to its distance from a straight Une (the directrix) is constant...

...Equation of the Second Degree Ax* + By2 + 2 Gx + 2 Fy + C = O. 85. The ellipse defined. An ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point, to its distance from a fixed line, is constant and less than unity. This...