 | George Salmon - Conic sections - 1852 - 329 pages
...the centres of circles described through the origin to touch the inverse curve. Thus from the theorem that the locus of the foot of the perpendicular from the focus on the tangent of a conic is a circle, we deduce (as Mr. Stubbs has pointed out) " the locus of the centre... | |
 | James Joseph Sylvester, James Whitbread Lee Glaisher - Mathematics - 1862 - 410 pages
...the equation to the projection of this sphero-conic and this is the equation to the circle which is the locus of the foot of the perpendicular, from the focus, on the tangent to the projection of the line of curvature (II). PROP. 2. The locus of the point of intersection... | |
 | W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...— b 2 for b 2 . 149. As in Art. 126, Also S0. = e*x - ae = e. SP, and S'G = e 2 i» +oe = e. /8'P. The locus of the foot of the perpendicular from the focus on the tangent is the circle described on AA' as diameter. 150. Corresponding to the formula jf = a 2 cos... | |
 | William Peveril Turnbull - Geometry, Analytic - 1867 - 298 pages
...•writing — J* for V. 149. As in Art. 126, CM.OT*-cf, Also SG = e*x-ae = e. SP, and S' G = e*x +ae=e. ST. The locus of the foot of the perpendicular from the focus on the tangent is the circle described on AA' as diameter. 150. Corresponding to the formula p* = a* cos*... | |
 | Thomas Grenfell Vyvyan - Geometry, Analytic - 1867 - 294 pages
...have x ( m + — ] = 0. .-. x= 0. Ч т) \ " This is the equation to the tangent at the vertex : hence the locus of the foot of the perpendicular from the focus on a tangent is the tangent at the vertex. 86. To find the equation of the chord of contact of tangents... | |
 | William Henry Besant - Conic sections - 1869 - 304 pages
...be perpendiculars drawn to the tangent and normal at any point, YZ i' parallel to the diameter. 24. Prove that the locus of the foot of the perpendicular from the focus on the normal is a parabola. 25. If PO be the normal, and GL the perpendicular from G upon SP, prove that GL is equal to the ordinate/W.... | |
 | James Maurice Wilson - 1872 - 160 pages
...FY '= YM and FA = AX, AY is parallel to the directrix, and is therefore the tangent at A. Therefore the locus of the foot of the perpendicular from the focus on the tangent is the tangent at the vertex. COR. 4. Since FYM is perpendicular to the tangent and FY = YM,... | |
 | Benjamin Williamson - Calculus, Differential - 1872 - 372 pages
...which the tangent at any point makes with the axis of y в is -. Here *? = ££ = cot?. am aх 2 dB 11. Prove that the locus of the foot of the perpendicular from the pole on the tangent to an equiangular spiral is the same curve turned through an angle. 12. Prove that... | |
 | Philip Kelland - 1873 - 248 pages
...the square of whose distance from a given line is proportional to its distance from a given plane. 3. Prove that the locus of the foot of the perpendicular from the centre on the tangent plane- of an ellipsoid is (ax)' + (by)' + (cz)' = (a? + if + z')'. 4. The sum... | |
 | George Salmon, Arthur Cayley - Curves, Algebraic - 1873 - 379 pages
...conic, a/3 = A*, becomes in the case of the parabola where A passes to infinity, /9cos0 = A, showing that the locus of the foot of the perpendicular from the focus /9 on a tangent is a right line. In like manner for a curve of the third class the formula 01/87 =... | |
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The locus of the foot of the perpendicular from the focus on a moving tangent is the circle on the major axis as diameter. 3. The locus of the point of intersection of perpendicular tangents is a circle with radius Va> 
