An Elementary Treatise on Conic SectionsMacmillan, 1883 - 352 sider |
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Side 57
... coincident . Hence the diagonal AC is cut harmonically . We can prove in a similar manner that the other diagonals are divided harmonically . INVOLUTION . * 61 . Def . Let O be a fixed point on a given straight line , and P , P ' ; Q ...
... coincident . Hence the diagonal AC is cut harmonically . We can prove in a similar manner that the other diagonals are divided harmonically . INVOLUTION . * 61 . Def . Let O be a fixed point on a given straight line , and P , P ' ; Q ...
Side 66
... coincident or imaginary . Hence there are two values of x , and the two corre- sponding values of y are found from ( ii ) . So that every straight line meets a circle in two real , coincident , or imaginary points - imaginary points ...
... coincident or imaginary . Hence there are two values of x , and the two corre- sponding values of y are found from ( ii ) . So that every straight line meets a circle in two real , coincident , or imaginary points - imaginary points ...
Side 67
... coincident if c = a√1 + m2 . Hence the line y = = mx + a√1 + m2 will touch the circle x + y = a for all values of m . Since either sign may be given to the radical / 1 + m2 , it follows that there are two tangents to a circle for ...
... coincident if c = a√1 + m2 . Hence the line y = = mx + a√1 + m2 will touch the circle x + y = a for all values of m . Since either sign may be given to the radical / 1 + m2 , it follows that there are two tangents to a circle for ...
Side 68
... coincident if the point be on the circle , and imaginary if the point be within the circle . Let the equation of the circle be x2 + y2 = a2 , and let h , k be the co - ordinates of any point . Let x ' , y ' be the co - ordinates of any ...
... coincident if the point be on the circle , and imaginary if the point be within the circle . Let the equation of the circle be x2 + y2 = a2 , and let h , k be the co - ordinates of any point . Let x ' , y ' be the co - ordinates of any ...
Side 69
... coincident , or imaginary according as པ་ ་ ་ a1h2 — a2 ( a2 — k3 ) ( h2 + k2 ) is greater than , equal to , or less than zero . That is , according as h2 + k2 - a2 That is , is greater than , equal to , or less than zero . according as ...
... coincident , or imaginary according as པ་ ་ ་ a1h2 — a2 ( a2 — k3 ) ( h2 + k2 ) is greater than , equal to , or less than zero . That is , according as h2 + k2 - a2 That is , is greater than , equal to , or less than zero . according as ...
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An Elementary Treatise on Conic Sections by the Methods of Co-ordinate Geometry Charles Smith Uten tilgangsbegrensning - 1921 |
Vanlige uttrykk og setninger
2hxy a² b2 angular points asymptotes ax² axes bisect by² Cambridge centre circumscribing coefficients College confocal conics conjugate diameters conjugate hyperbola constant corresponding cross ratio Crown 8vo curve diagonals directrix distance eccentric angles Edition ellipse envelope equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four points given points given straight line harmonic Hence imaginary inscribed latus rectum Let the co-ordinates Let the equation line joining line whose equation meet middle point nine-point circle normals pair of conjugate parabola pass pencil perpendicular point of intersection point Q points at infinity points of contact polar pole Professor projection prove quadrilateral radical axis rectangular hyperbola required equation right angles shew sides square subtend tangents triangle of reference values vertex zero
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