 | Benjamin Williamson - Calculus - 1873 - 394 pages
...tangent at the point makes with the axis of y is . Лу d9 в Here -^ = — = cot . dx м <te 2 " ii. 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. гг. Prove... | |
 | James White - Conic sections - 1878 - 160 pages
...and for any point inside the ellipse the sum of the focal distances is less than 2ci.) 81. To find the locus of the foot of the perpendicular from the focus on the tangent. Let P be the point where the perpendicular from the focus F, on any tangent TP, meets it.... | |
 | George Salmon - Curves, Algebraic - 1879 - 424 pages
...conic, a/3 = A*, becomes in the case of the parabola where A passes to infinity, /3cos0 = &, showing that the locus of the foot of the perpendicular from the focus /3 in a tangent is a right line. In like manner for a curve of the third class the formula a/Sy = AS... | |
 | James Russell Soley - Naval education - 1880 - 346 pages
...a conic section, the focns being the pole, and the equation to the tangent to it at any point. Find the locus of the. foot of the perpendicular from the focus on the tangent. 14. Prove that the locus of a point the sum of whose distances from two given points is constant... | |
 | Arthur Sherburne Hardy - Quaternions - 1881 - 252 pages
...vector to the point of contact. or (k) is also the perpendicular from the focus on the normal, and shows that the locus of the foot of the perpendicular from the focus on the normal is a parabola, whose vertex is at the focus of the given parabola and whose parameter is one-fourth that of the given... | |
 | Arthur Sherburne Hardy - Quaternions - 1881 - 248 pages
...vector to the point of contact. (fr) ¡s also the perpendicular from the focus on the normal, and shows that the locus of the foot of the perpendicular from the focus on the normal is aparábala, ivhose vertex is at the focus of the given parabola and whose parameter is one-fourth that... | |
 | Dublin city, univ - 1883 - 510 pages
...= o, find the numerical value of the symmetric function +!)(7 + «)08 + 5)(a + 0) (7 + 5). 10. Find the locus of the foot of the perpendicular from the focus on a normal of a parabola. ME. WR ROBERTS. 11. Prove that the circle circumscribing the triangle formed... | |
 | United States. Congress. Senate - United States - 1880 - 1304 pages
...a conic section, the focus being the pole, and tho equation to the tangent to it at any point. Find the locus of the foot of the perpendicular from the focus on the taugeiit. 14. Prove that the locus of a point the sum of whose distances from two given points is constant... | |
 | James Maurice Wilson - Conic sections - 1885 - 180 pages
...since 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,... | |
 | Sir Asutosh Mookerjee - Conic sections - 1893 - 197 pages
...given circle at P and Q. Construct a parabola which shall touch TP in P and have TQ for axis. Ex. 8. The locus of the foot of the perpendicular from the focus on the normal is a parabola. [Apply Prop. IV. SG is the axis, the vertex is at /S', the latus rectum— Ex. 9. If GK be drawn perpendicular... | |
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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> 
