 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>  Elements of Quaternions - Side 191av Arthur Sherburne Hardy - 1891 - 234 siderUten tilgangsbegrensning - Om denne boken
 | George Salmon - 1852 - 329 sider
...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 - 1862 - 410 sider
...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 - 1867 - 276 sider
...— 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 - 1867 - 298 sider
...•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 - 1867 - 294 sider
...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 - 1869 - 304 sider
...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 sider
...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,... | |
 | George Salmon, Arthur Cayley - 1873 - 379 sider
...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 =... | |
 | S. A. Renshaw - 1875 - 222 sider
...be perpendiculars to the tangent and normal at any point, YZ is parallel to the axis. 45. — Prove that the locus of the foot of the perpendicular from the focus on the normal is a Parabola. 46. — If E be the centre of the circle described about the triangle POp, (fig. 54) prove that the... | |
 | 1878 - 446 sider
...perpendicular from the focus on the normal is also — 7i3 -f- pj , whose expression just given proves that the locus of the foot of the perpendicular from...vertex is at the focus of the given parabola, and ivhose parameter is — of that of the given parabola. The vector to the middle point of a focal chord... | |
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