A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, Reader, and Dyer, 1869 - 377 páginas |
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Página ix
... values of k for which it represents right lines Equation of Conic passing through five given Points Equation of osculating Circle Equations of Conics having double contact with each other Every Parabola has a Tangent at infinity ( see ...
... values of k for which it represents right lines Equation of Conic passing through five given Points Equation of osculating Circle Equations of Conics having double contact with each other Every Parabola has a Tangent at infinity ( see ...
Página 8
... values for x and y given in the last article . х Ex . 1. The co - ordinates of a point satisfy the relation x2 + y2 - 4x - 6y = 18 : -- what will this become if the origin be transformed to the point ( 2 , 3 ) ? - - Ans . X2 + Y2 = 31 ...
... values for x and y given in the last article . х Ex . 1. The co - ordinates of a point satisfy the relation x2 + y2 - 4x - 6y = 18 : -- what will this become if the origin be transformed to the point ( 2 , 3 ) ? - - Ans . X2 + Y2 = 31 ...
Página 11
... values ( a , ) for x in the original equations , we get two equations in y , which must have a common root ( since the result of elimination be- tween the equations is rendered 0 by the supposition = a , ) . Let this common root be y ...
... values ( a , ) for x in the original equations , we get two equations in y , which must have a common root ( since the result of elimination be- tween the equations is rendered 0 by the supposition = a , ) . Let this common root be y ...
Página 12
... values of x and y can be found which will satisfy the given equation . And yet the co - ordinates of any point taken ... value of y , x = a , y = b ' , we should proceed as before , and we Y K P ' P M X should find a point P ' still ...
... values of x and y can be found which will satisfy the given equation . And yet the co - ordinates of any point taken ... value of y , x = a , y = b ' , we should proceed as before , and we Y K P ' P M X should find a point P ' still ...
Página 13
... value we please ( xa ) , and the equation will enable us to determine a finite number of values of y answering to this particular value of x ; and consequently , the equation will be satisfied for each of the points ( p , q , r , & c ...
... value we please ( xa ) , and the equation will enable us to determine a finite number of values of y answering to this particular value of x ; and consequently , the equation will be satisfied for each of the points ( p , q , r , & c ...
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Términos y frases comunes
anharmonic ratio asymptotes ax² axes bisected bisectors chord of contact circumscribing coefficients common tangents condition conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the co-ordinates find the equation find the locus fixed lines fixed point foci focus four points given circles given line given point Hence hyperbola imaginary points infinite distance inscribed intercept joining the points last Article length line at infinity line joining line meets meet the curve middle points origin parabola parallel Pascal's theorem perpendicular point of contact point x'y points at infinity points of intersection polar polar equation pole proved quadratic quadrilateral radical axis radius vector rectangle right angles right line second degree sides sin² square substituting tangential equation theorem values vanish vertex vertices