An Elementary Treatise on Conic Sections |
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Page 17
... straight line whose equation is given , it is only necessary to find the co- X ordinates of any two points on it . To do this we may give S. C. S. 2 to any two values whatever , and find from the THE STRAIGHT LINE . 17.
... straight line whose equation is given , it is only necessary to find the co- X ordinates of any two points on it . To do this we may give S. C. S. 2 to any two values whatever , and find from the THE STRAIGHT LINE . 17.
Page 28
... gives the bisector of the angle in which the origin lies . • 33. To find the equation of a straight line through the point of intersection of two given straight lines . The most obvious method of obtaining the required equation is to ...
... gives the bisector of the angle in which the origin lies . • 33. To find the equation of a straight line through the point of intersection of two given straight lines . The most obvious method of obtaining the required equation is to ...
Page 58
... ) * Ꭶ P q { PQRS } = { P'Q'R'S ' } . The above gives us at once a means of testing whether or not six points are in involution . For P , P ' will be con- jugate points in the involution determined by A , A 58 INVOLUTION . ”
... ) * Ꭶ P q { PQRS } = { P'Q'R'S ' } . The above gives us at once a means of testing whether or not six points are in involution . For P , P ' will be con- jugate points in the involution determined by A , A 58 INVOLUTION . ”
Page 68
... .......... . ( iii ) . - Equation ( iii ) gives the abscissae , and from ( i ) we get the corresponding ordinates . Since equation ( iii ) is a quadratic equation , there are two points the tangents at 68 THE CIRCLE .
... .......... . ( iii ) . - Equation ( iii ) gives the abscissae , and from ( i ) we get the corresponding ordinates . Since equation ( iii ) is a quadratic equation , there are two points the tangents at 68 THE CIRCLE .
Page 72
... give a geometrical construction for the polar of a point with respect to a circle . Let the equation of the circle be x2 + y2 = a2 ; let P be any point , and let the co - ordinates of P be x ' , y ' . The equation of the polar of P with ...
... give a geometrical construction for the polar of a point with respect to a circle . Let the equation of the circle be x2 + y2 = a2 ; let P be any point , and let the co - ordinates of P be x ' , y ' . The equation of the polar of P with ...
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Common terms and phrases
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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