An Elementary Treatise on Conic SectionsMacmillan and Company, 1894 - 352 sider |
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Side 8
... constant quantity a , and the abscissa of no other point is equal to a . Hence x = a is the equation of the line . Conversely the line drawn parallel to the axis of y and at a distance a from it is the locus of the equation x = α ...
... constant quantity a , and the abscissa of no other point is equal to a . Hence x = a is the equation of the line . Conversely the line drawn parallel to the axis of y and at a distance a from it is the locus of the equation x = α ...
Side 9
... constant ( 2c2 ) ; find the equation of its locus . Ans . x2 + y2 = c2 — a2 . Ex . 3. A point moves so that the difference of the squares of its distances from the two fixed points ( a , 0 ) and ( -a , 0 ) is constant ( c2 ) ; find the ...
... constant ( 2c2 ) ; find the equation of its locus . Ans . x2 + y2 = c2 — a2 . Ex . 3. A point moves so that the difference of the squares of its distances from the two fixed points ( a , 0 ) and ( -a , 0 ) is constant ( c2 ) ; find the ...
Side 15
... constants , whereas the equation found in Art . 15 only involves two . But if the co - ordinates x , y of any point ... constant . If we divide by B , we can write the equation y = — A B Ꮳ - C B ' and we have only the two A C constants ...
... constants , whereas the equation found in Art . 15 only involves two . But if the co - ordinates x , y of any point ... constant . If we divide by B , we can write the equation y = — A B Ꮳ - C B ' and we have only the two A C constants ...
Side 27
... ( ii ) , or on the negative side of both . If the equations are so written that the constant terms are both positive , the origin is on the positive side of both lines ; hence ( iv ) is the bisector of THE STRAIGHT LINE . 27.
... ( ii ) , or on the negative side of both . If the equations are so written that the constant terms are both positive , the origin is on the positive side of both lines ; hence ( iv ) is the bisector of THE STRAIGHT LINE . 27.
Side 31
... constant is a straight line . 35. A homogeneous equation of the nth degree will represent n straight lines through the origin . Let the equation be Ay " + By " 1x + Cy " 2x2 + ... + Kx " = 0 ...... . ( i ) . Divide by " and we get n A ...
... constant is a straight line . 35. A homogeneous equation of the nth degree will represent n straight lines through the origin . Let the equation be Ay " + By " 1x + Cy " 2x2 + ... + Kx " = 0 ...... . ( i ) . Divide by " and we get n A ...
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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 coincident common confocal conics conic touching conjugate diameters constant corresponding Crown 8vo curve diagonals director-circle directrix distance eccentric angles Edition ellipse equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four given points four points given conic given straight line imaginary inscribed latus rectum Let the equation line at infinity line joining line whose equation locus meet middle point nine-point circle normals original conic parabola Pascal's Theorem perpendicular point of intersection points at infinity points of contact polar pole Professor prove quadrilateral radical axis radius ratio rectangular hyperbola right angles second degree self-polar shew sides square tangential equation tangents triangle formed triangle of reference Trinity College values vertex vß² x² y² zero
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