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" 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... "
Gibson's London matriculation guide, by J. Gibson [and others]. - Page 11
1882
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The Elements of Coordinate Geometry: In Three Parts: 1. Cartesian Geometry ...

De Volson Wood - Geometry, Analytic - 1882 - 360 pages
...constant; show that the locus of the point is a circle. 30. Show that the locus is a circle when the point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant. 3?. If a point moves so that the sum of the squares...
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An Elementary Treatise on Analytic Geometry: Embracing Plane Geometry and an ...

Edward Albert Bowser - Geometry, Analytic - 1880 - 314 pages
...[Take the base and a perpendicular through its centre for axes.] Ans. x* + y* = s2 — m\ 23. A point moves so that the sum of the squares of its distances from the four sides of a square is constant; show that the locus of the point is a circle. CHAPTER V. THE...
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London graduation mathematics, questions in arithmetic and algebra set from ...

Thomas Kimber - 1880 - 176 pages
...radius of which is equal to a. Interpret each of the equations а? + y* = 0 and of — y* = 0. A point moves so that the sum of the squares of its distances from the three angles of a triangle is constant. Prove that it moves along the circumference of a circle....
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An elementary treatise on conic sections

Charles Smith - Conic sections - 1883 - 388 pages
...(5, - 2) are equal to one another ; find the equation of its locus. Ans. x-3?/ = l. Ex. 2. A point moves so that the sum of the squares of its distances from the two fixed points (a, 0) and ( - a, 0) is constant (2c2) ; find the equation of its locus. Ans....
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An Elementary Treatise on Conic Sections

Charles Smith - Conic sections - 1883 - 452 pages
...108, since SP — ePM, we have also S'P=e.NZ' = e(CZ'-CN) = a-ex; An ellipse is sometimes defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant. To find the equation of the curve from this definition....
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An Elementary Treatise on Solid Geometry

Charles Smith - Geometry, Analytic - 1884 - 256 pages
...locus of a point, whose distances from two given planes are in a constant ratio, is a plane. Ex. 10. The locus of a point, which moves so that the sum of its distances from any number of fixed planes is constant, is a plane. 21. The co-ordinates of any...
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Elements of analytic geometry

Simon Newcomb - Geometry, Analytic - 1885 - 488 pages
...curve does p = a cos (6 — a) + b cos (d — ft) + c cos (d — y) + . . . represent? 12. A point moves so that the sum of the squares of its distances from the four sides of a rectangle is constant. Show that the locus of the point is a circle. 13. Given...
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An Elementary Treatise on Solid Geometry

Charles Smith - Geometry, Analytic - 1886 - 268 pages
...locus of a point, whose distances from two given planes are in a constant ratio, is a plane. Ex. 10. The locus of a point, which moves so that the sum of its distances from any number of fixed planes is constant, is a plane. 21. The co-ordinates of any...
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Analytical Geometry (the Straight Line and Circle).

Arthur Le Sueur - Circle - 1886 - 120 pages
...axis itself is a diameter bisecting chords perpendicular to it. THE ELLIPSE. DEF. — An ellipse is the locus of a point which moves so that the sum of its distances from two fixed points ((he foci) is constant. Equation to an ellipse. S, S' the foci....
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Elements of Analytic Geometry

George Albert Wentworth - 1886 - 322 pages
...from the axis of x is half its distance from the origin ; find the equation of its locus. 20. A point moves so that the sum of the squares of its distances from the two fixed points (a, 0) and ( — a, 0) is the constant 2/fc2; find the equation of its locus....
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