An Elementary Treatise on Conic Sections |
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... equal to that of the range formed by their poles 329 Anharmonic properties of points on a conic , and of tangents to a conic 330 Homographic ranges and pencils 331 Two lines at right angles together with the lines to the circular points ...
... equal to that of the range formed by their poles 329 Anharmonic properties of points on a conic , and of tangents to a conic 330 Homographic ranges and pencils 331 Two lines at right angles together with the lines to the circular points ...
Page 1
... equal respectively to the known lines PM , PL and complete the parallelogram LOMP . The lengths MP and LP , or OL and OM , which thus define the position of the point P with reference to the S. C. S. 1 lines OX , OY are called the co ...
... equal respectively to the known lines PM , PL and complete the parallelogram LOMP . The lengths MP and LP , or OL and OM , which thus define the position of the point P with reference to the S. C. S. 1 lines OX , OY are called the co ...
Page 2
... equal to OM , and OL ' equal to OL , and through M ' , L ' draw lines parallel to the axes , as in the figure to Art . 1. Then the co - ordinates of the three points Q , R , S will be equal in magnitude to those of P. Hence it is not ...
... equal to OM , and OL ' equal to OL , and through M ' , L ' draw lines parallel to the axes , as in the figure to Art . 1. Then the co - ordinates of the three points Q , R , S will be equal in magnitude to those of P. Hence it is not ...
Page 8
... equal to c , the square of the distance OP will be equal to x + y2 [ Art . 4 ] . But OP is equal to the radius of the circle . Therefore the co - ordinates x , y of any point on the circle satisfy the relation 2 + y = c . That is , x2 + ...
... equal to c , the square of the distance OP will be equal to x + y2 [ Art . 4 ] . But OP is equal to the radius of the circle . Therefore the co - ordinates x , y of any point on the circle satisfy the relation 2 + y = c . That is , x2 + ...
Page 9
... equal to one another ; find the equation of its locus . - Ans . x - 3y = 1 . Ex . 2. A point moves so that the sum of the squares of its distances from the two fixed points ( a , 0 ) and ( −a , 0 ) is constant ( 2c2 ) ; find the ...
... equal to one another ; find the equation of its locus . - Ans . x - 3y = 1 . Ex . 2. A point moves so that the sum of the squares of its distances from the two fixed points ( a , 0 ) and ( −a , 0 ) is constant ( 2c2 ) ; find the ...
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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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