 | Henry Parr Hamilton - Mathematics - 1834 - 272 pages
...this property the equation to the ellipse may be deduced, as in the following Article : 117. To jlnd the locus of a point, whose distances from two fixed points are together always equal to a given quantity Za. Let S, H be the two fixed points, P the point whose locus... | |
 | George Salmon - Conic sections - 1852 - 329 pages
...circular points at infinity. Ex. 1. Mention has already been made (Art. 124) of the Cartesian oval, or the locus of a point whose distances from two fixed points are connected by the relation mp + np = d. This evidently becomes an ellipse or hyperbola when m = + n,... | |
 | James Robert Christie - Mathematics - 1866 - 428 pages
...any number of parallel chords is a straight line parallel to the axis of the parabola. 9. Show that the locus of a point whose distances from two fixed points are together always equal to a given line, is an ellipse of which the major axis is that line. II. ARITHMETIC... | |
 | Henry William Watson - Geometry - 1872 - 326 pages
...the points D and E coincide (Bk. VI. Prop. 7), therefore the points S and P coincide ; PROPOSITION n. The locus of a point whose distances from two fixed points are to each other in a given ratio is a certain circle. Let A and B be two given points, and let D be a... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...and through G draw GX | | to HB meeting AB produced in X. Then AX : XB as P : Q. PROBLEM (c). find the locus of a point whose distances from two fixed points are always in a constant ratio. Let A, B be the two fixed points. Join AB, and divide AB in F in the given... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...intersection of the given lines, if they intersect, and parallel to them, if the lines are parallel. ii. The locus of a point whose distances from two fixed points are in a constant ratio (not one of equality) is a circle. PROB. i. To divide a straight line similarly to a given divided... | |
 | James Maurice Wilson - 1878 - 450 pages
...and CD. Similarly there will be a line parallel to AB dividing BD externally in the same ratio. ii. The locus of a point -whose distances from two fixed points are in a constant ratio (not one of equality ) is a circle. Let A, C be the fixed points, and let B be one of the points on... | |
 | J. G - 1878 - 408 pages
...perimeters of similar polygons are to one another in the ratio of the homologous sides of the polygon. 2. The locus of a point whose distances from two fixed points are to each other in a given ratio is a certain circle. 3. // a line be drawn parallel to one iide of a... | |
 | Edward Harri Mathews - 1879 - 94 pages
...let fall on it from the opposite angle and the acute angle. By means of this proposition, show that the locus of a point, whose distances from two fixed points are in a constant ratio, is a circle. 3. If from any point without a circle two straight lines be drawn, one of which cuts the circle, and... | |
 | Thomas Kimber - 1880 - 176 pages
...The third bisects the angle between the other two. 17. Find, by elementary or co-ordinate geometry, the locus of a point whose distances from two fixed points are in a constant ratio, 18. At the points where the line - + ~- = 0 cuts the ellipse ab 2 2 x +У- =1 tangents are drawn. Find... | |
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The locus of a point whose distances from two fixed points are in a constant ratio (not one of equality) is a circle. 
