Geometry And Topology

Algebraic and Geometric Topology: Proceedings of a - download pdf or read online

By A. H. Assadi, P. Vogel (auth.), Andrew Ranicki, Norman Levitt, Frank Quinn (eds.)

ISBN-10: 3540152350

ISBN-13: 9783540152354

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Extra info for Algebraic and Geometric Topology: Proceedings of a Conference held at Rutgers University, New Brunswick, USA July 6–13, 1983

Sample text

Hallar las ecuaciones de las mediatrices del triángulo del Probleina 3. Sol. y 4- 3y -t 1 O. h ) Hallar el punto de intersección de dichas mediatrices. Sol. (-1918, 5/4). Este es el centro de la circunferencia circunscrita al triángulo. 5. a ) + 6. Demostrar que los puntos de interwcción de las medianas, de las alturai y de las mediatrices de los lados del triángulo del Problema 3, están en línea recta. Sol. 21 - 33y 7 46 = O. 7. Hallar la ecuación de la recta que pasa por el punto (2, 3) y cuya abscisa en el origen e i el doble q u e la ordenada en el origen.

Sol. U) U) U) (2, 2), b ) (1/2, 2), C ) 6, d ) x - 7/2 = O. (312, -7/4), b) (3/2, -4/3), C ) 5/3. (3/2. X = O. 7 . Hallar la ecuación de una parábola cuyo eje sea paralelo al eje x y que pase por los puntos (3, 3), (6, 5) y (6, --3). SO/. v - 4 . ~+ 9 O. 8. Hallar la ecuación de una parábola de eje vertical y que pase por los puntos (4, 5), (-2, IO := o. Sol. x 2 - 4 s - 2y + I I ) y(-4, 21). 9. Y, y que pase por los puntos ( 3 , 5) y (6, --I). SO/. \- --iI 7 =-- O, I 1-P- 981' - 1 0 8 ~-t 539 = O.

3 Como el centro es el punto (-1, --I) y el vértice (5, -1) se tiene, a = 6, e = -c = -c = -2- a de donde c = 4. 6 , 3 Por otra parte, b2 = a2- c2 = 36 - 16 = 20. + (x ]I2 La ecuación pedida es ~- 36 (Y + + -~ 20 - 12. Hallar la ecuación de la elipse cuya directriz es la recta x = -1, uno de los focos el punto (4, -3) y excentricidad 213. De la definición general de sección cónica, si PF PM ~- = e y e < 1 la curva es una elipse. _____ I +I I 2 -- 3' Elevando al cuadrado los dos miembros de esta ecuación y simplificando resulta, x + l OI l l x -+ 9y2 - 8 0 -+~ 54y = -221.

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Algebraic and Geometric Topology: Proceedings of a Conference held at Rutgers University, New Brunswick, USA July 6–13, 1983 by A. H. Assadi, P. Vogel (auth.), Andrew Ranicki, Norman Levitt, Frank Quinn (eds.)


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