...positive part of the x-axis. Find the coordinates of the other vertices if a side is 10. 11. What is the locus of a point which moves so that the ratio of its ordinate to its abscissa is always 1 ? So that this ratio is always — 1 ? Always 2? Write the equations....

...which removes two of the terms of the given equation. CHAPTER VII THE PARABOLA 112. Conic Section. The locus of a point which moves so that the ratio of its distances from a fixed point and a fixed line is constant is called a conic section, or simply a conic. We shall designate the moving...

...fixed circle from the point, to the distance of the point from a fixed line is constant? 10. What is the locus of a point which moves so that the ratio of the square of its distance from a fixed line to its distance from another line is constant? 11. Find...

...parallels meet at E; prove that a parallel to BC through E, meeting AB, CD, is bisected at E. Ex. 47. Find the locus of a point which moves so that the ratio of its distances from two intersecting straight lines is constant. Ex. 48. ABCD is any parallelogram. From A a straight line...

...is the locus of a point equidistant from a plane and a line perpendicular to the plane? 7. What is the locus of a point which moves so that the ratio of its distances from two perpendicular intersecting lines is constant ? 9. The sum of the distances of a point from three...

...unequal, the triangle which has the greater >u.--- angle has the greater third side. 2 12 Problem: To find the locus of a point which moves so that the ratio of its distance Я two fixed points, Л and В, is constant and equal to m [in the construction s* m-Ü. 3...

...conic which is mathematically equivalent to the geometrical definition above: A conic is a circle or the locus of a point which moves so that the ratio of its absolute distance from a given point (a focus) to its absolute distance from a given line (a directrix)...

...the power of a point P with respect to a point-circle, center A, is equal to PA=2. Hence determine the locus of a point /"which moves so that the ratio of its distances PA=:=PA' from two given points A, A' is constant. 27.2 Determine the locus of the previous Exercise...

...paraboloid. This is the surface generated by revolving a parabola about its axis. The hyperbola is the locus of a point which moves so that the ratio of its distances from the focus and directrix is constant and greater than 1 . The eccentricity is thus greater than 1 ....

...nucleus of a heavy atom. Apollonius first recognized what all the conic sections have in common. Each is the locus of a point which moves so that the ratio of its distance (/) from a fixed point (the focus F) to its distance (d) from a straight line (the directrix)...