An Elementary Treatise on Conic Sections |
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Page 88
... eccentricity . It will be shewn hereafter [ Art . 312 ] that if a right circular cone be cut by any plane , the section will be in all cases a conic as defined above . It was as sections of a cone that the properties of these curves ...
... eccentricity . It will be shewn hereafter [ Art . 312 ] that if a right circular cone be cut by any plane , the section will be in all cases a conic as defined above . It was as sections of a cone that the properties of these curves ...
Page 120
... eccentricity is and shew that the origin is at an extremity of the minor axis . - 1 , 1 ) for 10. Find the equation of the ellipse which has the point focus , the line 4x - 3y = 0 for directrix , and whose eccentricity is § . Ans . 20x2 ...
... eccentricity is and shew that the origin is at an extremity of the minor axis . - 1 , 1 ) for 10. Find the equation of the ellipse which has the point focus , the line 4x - 3y = 0 for directrix , and whose eccentricity is § . Ans . 20x2 ...
Page 123
... a constant ratio to one another . The angle A'Cp is called the eccentric angle of the point P. The point p on the auxiliary circle is said to correspond to the point P on the ellipse . If the angle A'Cp be p , the co - THE ELLIPSE . 123.
... a constant ratio to one another . The angle A'Cp is called the eccentric angle of the point P. The point p on the auxiliary circle is said to correspond to the point P on the ellipse . If the angle A'Cp be p , the co - THE ELLIPSE . 123.
Page 124
... eccentric angles are given . Let , ' be the eccentric angles of the two points ; then the co - ordinates are a cos p , b sin 4 , and a cos p ' , b sin respectively . or x .. α Hence the equation of the line joining them is = y - b sin o ...
... eccentric angles are given . Let , ' be the eccentric angles of the two points ; then the co - ordinates are a cos p , b sin 4 , and a cos p ' , b sin respectively . or x .. α Hence the equation of the line joining them is = y - b sin o ...
Page 125
... eccentric angle of the point . Let be the eccentric angle of a point P on the ellipse ; the equation of the tangent at P is [ Art . 122 ] ac cos + 2 / sin 6 = 1 . a The equation of the line through ( a cos d , b sin 4 ) perpendicular to ...
... eccentric angle of the point . Let be the eccentric angle of a point P on the ellipse ; the equation of the tangent at P is [ Art . 122 ] ac cos + 2 / sin 6 = 1 . a The equation of the line through ( a cos d , b sin 4 ) perpendicular to ...
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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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