An Elementary Treatise on Conic Sections |
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Page 12
... Hence y = b is the equation of the line . Similarly a is the equation of a straight line parallel to the axis of y and at a distance a from it . 14. To find the equation of a straight line which passes through the origin . Let OP be a ...
... Hence y = b is the equation of the line . Similarly a is the equation of a straight line parallel to the axis of y and at a distance a from it . 14. To find the equation of a straight line which passes through the origin . Let OP be a ...
Page 26
... Hence the length of the perpendicular from any point on the line x cos a + y sin a - p = 0 is obtained by substi- tuting the co - ordinates of the point in the expression - x cos a + y sin a — p . x The expression a ' cos a + y ' sin a ...
... Hence the length of the perpendicular from any point on the line x cos a + y sin a - p = 0 is obtained by substi- tuting the co - ordinates of the point in the expression - x cos a + y sin a — p . x The expression a ' cos a + y ' sin a ...
Page 27
... Hence , if the equations of the lines be = = 0 ....... ax + by + c a'x + by + c = 0 .. and ( x , y ) be any point on either of the bisectors , ax ' + by ' + c a'x ' + b'y ' + c ' and √a + b2 must be equal in magnitude . α √a'2 + b22 ...
... Hence , if the equations of the lines be = = 0 ....... ax + by + c a'x + by + c = 0 .. and ( x , y ) be any point on either of the bisectors , ax ' + by ' + c a'x ' + b'y ' + c ' and √a + b2 must be equal in magnitude . α √a'2 + b22 ...
Page 28
... Hence ( iii ) is the equation of a straight line passing through the point of intersection of the given lines . Also by giving a suitable value to λ the equation may be made to satisfy any other condition , it may for example be made to ...
... Hence ( iii ) is the equation of a straight line passing through the point of intersection of the given lines . Also by giving a suitable value to λ the equation may be made to satisfy any other condition , it may for example be made to ...
Page 42
... Hence , [ Art . 26 ] the angular points of the triangle are either all on the positive sides of the lines ( i ) , ( ii ) , ( iii ) , or all on the negative sides . The perpendiculars from the centre of the inscribed circle on the sides ...
... Hence , [ Art . 26 ] the angular points of the triangle are either all on the positive sides of the lines ( i ) , ( ii ) , ( iii ) , or all on the negative sides . The perpendiculars from the centre of the inscribed circle on the sides ...
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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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