 | George Cunningham Edwards - 1895 - 330 sider
...a parallelogram, which may be converted into a square. Illustration. — The locus of a point which moves in a plane so that the ratio of its distances from a fixed point and from a fixed line equals 1 generates what is called a parabola. If through any point... | |
 | Alexander Russell - 1904 - 428 sider
...(1), or — = constant. Now by a well-known geometrical theorem the locus of a point P which moves so that the ratio of its distances from two fixed points A and B is constant, is a circle, and if C be its centre and r its radius, CA.CB = r* (2). These points... | |
 | Edwin Schofield Crawley, Henry Brown Evans - 1918 - 257 sider
...0, (c) (4 + ^)z2 + 3?/2 + (3 + 4i)x + 4 + 5i = 0, (d) z2 + 2?/2 + is - Ziy + 6 - 7i = 0. 7. A point moves in a plane so that the ratio of its distances from the points (2, 4) and (—3, 7) is always as 1 to 3. Find the equation of its locus. Ans. 4z2 + 4?/2... | |
 | Winfield Paul Webber, Louis Clark Plant - 1919 - 330 sider
...has been of much value in the study of the laws of nature. Definition. — The locus of a point which moves in a plane so that the ratio of its distances from a fixed point and a fixed straight line is constant is called a conic section * or for short a conic.... | |
 | University of Kansas - 1902 - 382 sider
...place, let c — o; we then have r'=pr, where p is a constant. The locus of a point z, which moves so that the ratio of its distances from two fixed points A and A' is a constant, is a circle having A and A' for a pair of inverse points. Hence, the path curves... | |
 | Euclid - 1908 - 196 sider
...into two parts so that the chords of these parts may be to each other in a given ratio. 47. A point /' moves in a plane so that the ratio of its distances...externally in the given ratio. What is the exceptional case ? 48. The side BC of a triangle ABC is bisected at D, and the angles ADC, ADB are bisected by the straight... | |
 | 352 sider
...equations of the tangent to C at the origin and of the line through the centres of the circles. 32. A point P moves in a plane so that the ratio of its distances from two fixed points A, B in the plane is constant. Prove that its locus is a circle. If PA/PB = A > 1, and AB = 2a, prove that... | |
 | G. P. West - 1965 - 362 sider
...CA, AB in P, Q, R respectively. Prove that BP CQ AR PC QA* RB ' 10. Apollonius' Circle. A point moves so that the ratio of its distances from two fixed points, A and B, is constant. Prove that its locus is a circle. [If P is any position of the point, draw the... | |
 | Ray C. Jurgensen, Alfred J. Donnelly, Mary P. Dolciani - 1963 - 198 sider
...orthogonal to the given circle. SECTION II. THE CIRCLE OF APOLLONIOS*. THEOREM 37. If a point P moves so that the ratio of its distances from two fixed points a, R is constant, the locus of P is a circle. fig. 45. For any position of P draw PX, PY, the bisectors... | |
 | Military Academy, West Point - 906 sider
...greater included angle has the greater third side. 12 Problem : To find the locus of a point which moves so that the ratio of its distances from two fixed points. A and B. Is constant and equal to in [In the construction makes in=y¿\. 10 Theorem : If, through a point... | |
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P moves in a plane so that the ratio of its distances from two fixed points A, B in that plane is always the same. 