 | Queen's University of Belfast - 1852 - 306 σελίδες
...joining their centers cuts it at right angles. 4. Find the polar equation to the locus of a point whose distance from a fixed point bears a constant ratio to its distance from a fixed right line. Deduce from the equation the three forms of this locus for different values of the ratio.... | |
 | Isaac Todhunter - 1855 - 332 σελίδες
...bisects MN. CHAPTER XI. THE HYPERBOLA. 209. To find the equation to the hyperbola. The hyperbola is the locus of a point which moves so that its distance...ratio to its distance from a fixed straight line, the ratio being greater than unity. B' Let H be the fixed point, YY' the fixed straight line. Draw... | |
 | Isaac Todhunter - 1858 - 334 σελίδες
...definitions, and investigate some of their properties from their equations. DBF. A conic section is the locus of a point which moves so that its distance...ratio to its distance from a fixed straight line. If this ratio be unity, the curve is called a parabola, if less than unity, an ellipse, if greater... | |
 | W. P. Turnbull - 1867 - 276 σελίδες
...line joining the other two. (Ex. 29, Chap, vi.) CHAPTER VIII. THE PARABOLA. 103, A conic section is the locus of a point which moves so that its distance...ratio to its distance from a fixed straight line. The conic section is a parabola, an ellipse, or a hyperbola, according as this constant ratio is equal... | |
 | Philip Kelland - 1873 - 248 σελίδες
...straight lines which do not meet ; find the locus of its centre. CHAPTER VI. THE ELLIPSE. 43. !• IF we define a conic section as "the locus of a point...we shall find the equation to be (Ex. 5, Art. 35) аУ = е'(а"-8ар)' ........................ (1), where SP = ePQ, vector SD = a, SP = p. When e... | |
 | R. M. Milburn - 1880 - 116 σελίδες
...2a -, focus the pole. i+cos (ii) r= 4a.c°sy-, vertex the pole. THE ELLIPSE. 56. Def. The ellipse is the locus of a point which moves so that its distance...ratio to its distance from a fixed straight line, the ratio being less than unity. Foci S, H; centre C ; axis major A'CA=2a; axis minor BCB'=2b. 57.... | |
 | Edward Albert Bowser - 1880 - 334 σελίδες
...and interest to the right line and circle. A Conic Section is the locus of a point moving in a plane so that its distance from a fixed point bears a constant ratio to its distance from a fixed right line. If this ratio is unity, the locus is a Parabola; if less than unity an Ellipse; if greater... | |
 | Hussein Tevfik (Pacha.) - 1882 - 98 σελίδες
...equation of a sphere. The equation of a Conic Section deduced directly from its definition. 85. We will define a Conic Section as the locus of a point which...constant ratio to its distance from a fixed straight lens. (Kelland and Tait, Art. 43). Let F be the given point, DQ the given straight line, = e PQ the... | |
 | Henry Percy Smith - 1883 - 542 σελίδες
...natural state as to be fit recipients of it. (Condignity.) CONE 135 CONS it moves in such a manner that its distance from a fixed point bears a constant ratio to its perpendicular distance from a fixed line. The fixed point is called the/a««, the fixed line the directrix... | |
 | George Albert Wentworth - 1886 - 322 σελίδες
...Their equations are y -\- 2x + 1 = 0, and y — 3x = 0. 195. A Conic is the locus of a point whose distance from a fixed point bears a constant ratio to its distance from a fixed straight line. 196. To find the equation of a conic. r Fig. 78. e the constant ratio ; then FP -H NP = e, P being... | |
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IF we define a conic section as "the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line 
