 | Sir George Greenhill - Calculus - 1891 - 488 pages
...is a parabola. But we can easily show that the curve OP satisfies the definition of a parabola as " the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line" by making the angle TOS equal to the angle TOH,... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...theorem is much used in earth-work. BOOK IX. CONIC SECTIONS. THE PARABOLA. 791. The curve traced by a point which moves so that its distance from a fixed point is always equal to its distance from a fixed line is called a parabola. The curve lies in the plane... | |
 | Robert Lachlan - Geometry - 1893 - 312 pages
...The Reciprocal of a circle. 297. It was proved in § 294 that the reciprocal curve of a given circle is the locus of a point which moves so that its distance from the centre of reciprocation varies as its distance from the line which is the reciprocal of the centre... | |
 | W. J. Johnston - Geometry, Analytic - 1893 - 448 pages
...2 PB find the eq'n to the locus of P. Ans. 3 x3 + 3 y2 — IQ ax + 3 a2 =• о 4. Find the eq'n to the locus of a point which moves so that its distance from the origin •« twice its distance from the axis of x. Ans. The two lines x + y v'î = °5. Find the... | |
 | George Albert Wentworth - 1894 - 362 pages
...centre of the given hyperbola. 23. The distance from a fixed point to a fixed straight line is 10. Find the locus of a point which moves so that its distance from the fixed point is always twice its distance from the fixed line. I. Solution. From § 183, the locus... | |
 | Sidney Luxton Loney - Coordinates - 1896 - 447 pages
...15. PQ is a double ordinate of a parabola. Find the locus of its points of trisection. 16. Prove that the locus of a point, which moves so that its distance from a fixed line is equal to the length of the taogent drawn from it to a given circle, is a parabola. Find the... | |
 | Frederick Harold Bailey - Geometry, Analytic - 1897 - 392 pages
...even though this requires more time. We shall adopt the usual definition of a circle, ie, The circle is the locus of a point which moves so that its distance from a fixed point, called the centre, shall be constant, this constant distance being called the radius. Let P(x, y), Pig. 45, be... | |
 | Sidney Luxton Loney - Coordinates - 1897 - 472 pages
...15. PQ is a double ordinate of a parabola. Find the locus of its points of trisection. 16. Prove that the locus of a point, which moves so that its distance from a fixed line is equal to the length of the tangent drawn from it to a given circle, is a parabola. Find the... | |
 | John Henry Tanner, Joseph Allen - Geometry, Analytic - 1898 - 484 pages
...the curves. I. THE PARABOLA Special Equation of Second Degree C = 0, or 102. The parabola defined, A parabola is the locus of a point which moves so...called the focus, is equal to its distance from a fixed line, called the directrix. It is the conic section with eccentricity e = 1 (cf. Art. 48). The equation... | |
 | John Henry Tanner, Joseph Allen - Geometry, Analytic - 1898 - 458 pages
...Special Equation of Second Degree C = 0, or Byz 102. The parabola defined, A parabola is the locus oí a point which moves so that its distance from a fixed...called the focus, is equal to its distance from a fixed Hue, called the directrix. It is the conic section with eccentricity e=l (cf. Art. 48). The equation... | |
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Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig. 
