An Elementary Treatise on Conic SectionsMacmillan, 1883 - 352 sider |
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Side 81
... series of co - axial circles pass through another fixed point , and the polar of one of the limiting points of the system is the same for all the circles . The system of circles is given by the equation x2 + y2 + 2ax + c = 0 .. where c ...
... series of co - axial circles pass through another fixed point , and the polar of one of the limiting points of the system is the same for all the circles . The system of circles is given by the equation x2 + y2 + 2ax + c = 0 .. where c ...
Side 138
... series of ellipses are described with a given focus and corresponding directrix ; shew that the locus of the extremities of their minor axes is a parabola . 6. PNP ' is a double ordinate of an ellipse , and Q is any point on the curve ...
... series of ellipses are described with a given focus and corresponding directrix ; shew that the locus of the extremities of their minor axes is a parabola . 6. PNP ' is a double ordinate of an ellipse , and Q is any point on the curve ...
Side 165
... series of chords of the hyperbola x2 y2 a2 - b3 = 1 are tangents to the circle described on the straight line joining the foci of the hyperbola as diameter ; shew that the locus of x2 y3 1 their poles with respect to the hyperbola is + ...
... series of chords of the hyperbola x2 y2 a2 - b3 = 1 are tangents to the circle described on the straight line joining the foci of the hyperbola as diameter ; shew that the locus of x2 y3 1 their poles with respect to the hyperbola is + ...
Side 178
... series of conics are described with a common latus rectum ; prove that the locus of points upon them , at which the perpendicular from the focus on the tangent is equal to the semi - latus rectum , is given by the equation / = -r cos 20 ...
... series of conics are described with a common latus rectum ; prove that the locus of points upon them , at which the perpendicular from the focus on the tangent is equal to the semi - latus rectum , is given by the equation / = -r cos 20 ...
Side 248
... series of confocal conics is a straight line . Let the equation of the confocals be x2 + a2 + λ y2 6 ° + 入: 1 ....... and let the equation of the given straight line be lx + my = .. ( i ) , ... ( ii ) . The equation of the polar of the ...
... series of confocal conics is a straight line . Let the equation of the confocals be x2 + a2 + λ y2 6 ° + 入: 1 ....... and let the equation of the given straight line be lx + my = .. ( i ) , ... ( ii ) . The equation of the polar of the ...
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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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