...whole line. 5. Given the base, area, and one of the angles at the base, construct the triangle. 6. Find the locus of a point which moves so that the sum of the squares of its distance from four given points is constant. On the Quadrature of a Rectilineal...

...given point parallel to a given plane ? parallel to a given line ? in. ANALYTIC GEOMETRY. 1. Determine the locus of a point which moves so that the sum of the Hquares of its distances from two fixed points is constant. Also determine the locus, changing...

...determine whether the straight line x + У = 2 +-/2 is a tangent or not. 17. Find the locus of a point, P, which moves so that the sum of its distances from two fixed points, A and B, is constant. 1870. July 19th. — Examiners, — Prof. HJS SMITH, MA, FRS, and Prof. SYLVESTER,...

...II. THE ELLIPSE. Definitions. 9. An ellipse is a plane curve that may be generated by a point, moving so that the sum of its distances from two fixed points is equal to a given line. The moving point is called the generatrix; the fixed points are foci ; the straight...

...fixed points. In what case does the conic degenerate into two intersecting straight lines ? 45. Find the locus of a point which moves so that the sum of the squares on the tangents drawn from it to the ellipse, -—- - + —jf = 1, is constant. X a v'...

...of the perpendiculars from any other point P, will bisect OP. [Such a polygon has the property that the locus of a point, which moves so that the sum of the squares on its distances from the sides is constant, is a circle.] 2254. The limiting position...

...that the difference of the distances of any point in either brunch of Fig. 12.— Hyperbola, the curve from two fixed points, is constant. The fixed points are the foci of the curves. The heavenly bodies all move in conic sections; the path of each of the planets is an...

...determine whether the straight line x + у = 2 +\/2 is a tangent or not, 17. Find the locus of a point, P, which moves so that the sum of its distances from two fixed points, A and B, is constant, 1870. July 19th. — Examiners, — Prof. HJS SMITH, MA, FRS, and Prof. SYLVESTER,...

...process as often as is required. Def.—An ellipse is the locus of a point which moves in such a way that the sum of its distances from two fixed points is constant. This accurate mathematical definition merely means that an ellipse is a curve traced out by the point...

...cut the curve will be the extremities of conjugate diameters. 105. If a point move in such a manner that the sum of its distances from two fixed points is constant, prove that its distance from any one bears a constant ratio to its distance from some fixed line. 106....