 | George Salmon - Conic sections - 1855 - 376 pages
...xy'' = (& - b3 - c2) (yz - 6s), or x* y» _ i-' + c* fri Ex. 2. Kind the envelope of a line such that the sum of the squares of the perpendiculars on it from two fixed points mav be constant. ** y2 Ani- r, — "* + » = 10> — c2 62 Ex. 3. Find the envelope if the difference... | |
 | Robert Henry Wright - Coordinates, Trilinear - 1865 - 174 pages
...the conies are .y' = aß and -r^L- - aß = 0. sin" 20 ' 160. Find the envelope of a line such that the sum of the squares of the perpendiculars on it from two fixed points may be constant. 161. Find the envelope if the difference of squares of perpendiculars be given. The... | |
 | Benjamin Williamson - Calculus, Differential - 1872 - 372 pages
...find the envelope of the opposite side when the area is given. 3. Find the envelope of a line when the sum of the squares of the perpendiculars on it from two given points is constant. 4. Find the envelope of a right line, when the rectangle under the perpendiculars... | |
 | Benjamin Williamson - Calculus - 1873 - 394 pages
...find the envelope of the opposite side when the area is given. 3. Find the envelope of a line when the sum of the squares of the perpendiculars on it from two given points is constant. 4. Find the envelope of a right line, when the rectangle under the perpendiculars... | |
 | Civil service - 1878 - 228 pages
...analytically or geometrically, that A Yj and AYa are together equal to the distance of P from the axis. 5. A straight line moves so that the sum of the squares of its distances from the two points A and B at a distance 2a apart is equal to rf2. Prove, either analytically... | |
 | W. J. Johnston - Geometry, Analytic - 1893 - 448 pages
...circle. 30. The envelope of a circle on a chord of a conic fixed in direction as diameter is a conic. 31. A straight line moves so that the sum of the squares of the perpendiculars on it from any number of fixed points is constant : prove that its envelope is a conic. 32. If the normals drawn... | |
 | Sir Horace Lamb - Calculus - 1897 - 644 pages
...the a? y* ellipse -5 + p = 1 as diameters : prove that the envelope is the ellipse a" + 6" 62— 13. A straight line moves so that the sum of the squares of the perpendiculars on it from the fixed points (+ c, 0) is constant ( = 2A-) ; prove that the envelope is the conic and examine the... | |
 | Daniel Alexander Murray - Calculus - 1908 - 522 pages
...are a and 6 : show that their envelope is the co-axial ellipse whose semi-axes are Va2 + 62 and 6. 9. About the points on a fixed ellipse as centre,...ellipse. 10. A straight line moves so that the sum o£ the squares of the perpendiculars on it from two fixed points (± c, 0) is constant (= 2 &2) :... | |
 | 556 pages
...3 + 55 •= ! a2 6" as diameters : prove that the envelope is the ellipse ,y' _! «' + 6' /»" 16. A straight line moves so that the sum of the squares of the perpendiculars on it from the fixed points (+ c, 0) is constant (= '2k'1) ; prove that the envelope is the conic and examine... | |
 | 558 pages
...double ordinates of the ellipse as diameters : prove that the envelope is the ellipse * .У' ! ~ 16. A straight line moves so that the sum of the squares of the perpendiculars on it from the fixed points (+ c, 0) is constant (= 2A2) ; prove that the envelope is the conic tf-c2 /t»~ '... | |
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A straight line moves so that the sum of the squares of the perpendiculars on it from two fixed points (± c, 0) is constant (= 2fc'2) : show that y2 y'2 its envelope is the conic — - ( + ^ = 1. 